As the students were approaching the park, they noticed a huge tower that was just
being completed. Lucas and Jacob were part of the group responsible for looking at
advertising. They couldn’t help but to think, one of the main attractions of the park
would be the ride involving this tower. It was a bright, sunny day. As they got off
the bus, they collected the mathematical materials provided by their teacher. These
materials included: pencil, paper, eraser, calculator, measuring tape, a
clinometer (a tool used to measure vertical angles). They walked through the
park until they reached the shadow of the tower. They looked up and couldn’t
believe how high it was
Q: If they are going to advertise, the height of the tower in a brochure that is
being created, they want to be sure of their answer. Describe how they
could use the materials they have and trigonometry to determine the
height of the tower. The explanations should include a detailed diagram,
clear step by step instructions making use of terminology appropriately
and even examples showing the calculations to be used to determine
the height.
Answers
The students could use what they know of triangle rectangles, in the image below you can see the diagram that the students could use to estimate the height of the tower.
First, the students could use the measuring tape to find the distance between the base of the tower and them, this distance is represented with the variable S in the image below.
Now, using the clinometer, they could find the elevation angle between their viewpoint and the tip of the tower. This would be the angle θ in the image (notice that they should do this from the ground).
So at this point, we know one angle and the adjacent cathetus to that angle.
And we want to find the height of the tower, which is the opposite cathetus to the known angle.
Then we can remember the trigonometric relation:
tan(a) = (opposite cathetus)/(adjacent cathetus)
Replacing these by the things we know:
tan(θ) = H/S
tan(θ)*S = H
Then, by measuring θ and S, we can find the height.
If you want to read more about triangle rectangles, you can see:
https://brainly.com/question/16893462
Related Questions
What is the translation from the preimage to the image in the graph?
Answers
Answer:
(x, y ) → (x + 4, y - 1 )
Step-by-step explanation:
Consider the coordinates of K and K'
K (- 3, 5 ) , K' (1, 4 )
x- direction : - 3 → 1 is + 4 units to the right
y- direction : 5 → 4 is - 1 units down
translation rule is (x, y ) → (x + 4, y - 1 )
Diseases I and II are prevalent among people in a certain population. It is assumed that 11% of the population will contract disease I sometime during their lifetime, 16% will contract disease II eventually, and 2% will contract both diseases. (a) Find the probability that a randomly chosen person from this population will contract at least one disease. .25 Correct: Your answer is correct. (b) Find the conditional probability that a randomly chosen person from this population will contract both diseases, given that he or she has contracted at least one disease. (Round your answer to four decimal places.)
Answers
Answer:
a) [tex]P(A \cup B)=0.23[/tex]
b) [tex]P(X)=0.87[/tex]
Step-by-step explanation:
From the question we are told that:
Probability of contacting disease 1 [tex]P(1)=0.11[/tex]
Probability of contacting disease 2 [tex]P(2)=0.16[/tex]
Probability of contacting both disease [tex]P(1\& 2)=0.2[/tex]
a)
Generally the equation for a Random contact is mathematically given by
[tex]P(A \cup B)=P(1)+P(2)-P(A \cap B)[/tex]
[tex]P(A \cup B)=\frac{11}{100}+\frac{16}{100}-\frac{4}{100}[/tex]
[tex]P(A \cup B)=\frac{11+16-4}{100}[/tex]
[tex]P(A \cup B)=0.23[/tex]
b)
Generally the equation for Probability of contacting both after having contacted one is mathematically given by
[tex]P(X)=\frac{P(1\& 2)}{P(A \cup B)}[/tex]
Therefore
[tex]P(X)=\frac{0.2}{0.23}[/tex]
[tex]P(X)=0.87[/tex]
find the missing length for the following trapezoid
Answers
Answer:
15 is the answer I think.
428363939+42724289292952926263938
Answers
Answer:
4.2724289e
+22
Step-by-step explanation:
mzmznznxnxnznxn no n n j j h h h h h h hh h h &
Need help ASAP rocky ! Help needed
Answers
Answer:
x/x∈R,x≤5 1/6
Step-by-step explanation:
What is the equation of a line, in slope-intercept form, that has a slope of 3 and contains the point (0,5)?
Answers
That is slope intercept form.
m= slope, which is 3
b= y-int, which is 5.
The y intercept is the value of y/ coordinate where the function intercepts the y axis. The y int is where x=0. In this case, y=5 when x=0.
Then just substitute those numbers into the equation.
y=3x+5
Complete the table of values of y = 14 x + 1.
Answers
Answer:
-4,0
0,1
8,3
======
x: -4, 0, 8
f(x) = 1/4(x) + 1
Plug in x values into f(x)...
f(-4) = 0
f(0) = 1
f(8) = 3
If m∠A = 43° and the measure of arc AB = 69°, then m∠B = ° (Blank 1). (Round your answer to one decimal place, if necessary.)
Answers
====================================================
Explanation:
If angle A is 43 degrees, then minor arc BC is 2*43 = 86 degrees according to the inscribed angle theorem. The central angle is twice that of the inscribed angle. Both of these angles subtend the same minor arc.
When I say "minor arc BC", I mean that we go from B to C along the shortest path. Any minor arc is always less than 180 degrees.
Since minor arc AB is 69 degrees, and minor arc BC is 86 degrees, this means arc ABC is arcAB+arcBC = 69+86 = 155 degrees
Let's say point D is some point on the circle that isn't between A and B, and it's not between B and C either. Refer to the diagram below. The diagram is to scale. The diagram your teacher provided is not to scale because arc ABC is way too big (it appears to be over 180 degrees). Hopefully the diagram below gives you a better sense of what's going on.
Because arc ABC = 155 degrees, this means the remaining part of the circle, arc ADC, is 360-(arc ABC) = 360-155 = 205 degrees
Inscribed angle B subtends arc ADC. So we'll use the inscribed angle theorem again, but this time go in reverse from before. We'll cut that 205 degree angle in half to get 205/2 = 102.5 degrees which is the measure of angle B. This value is exact. In this case, we don't need to apply any rounding.
Sandra has developed a program designed to increase reading comprehension scores in 6th graders. She randomly selects three students and has them participate in her program. When she compares the mean score from the students who completed her program to three students who did not participate in the program, she finds no significant difference between their mean scores. What is most likely the reason for the non-significant finding
Answers
Answer:a small sample size
Step-by-step explanation:
From the information given in the question, we are informed that Sandra developed a program that was designed to increase reading comprehension scores in 6th graders and she then randomly selects three students and has them participate in her program.
After comparing the mean score from the students who completed her program to three students who did not participate in the program, she finds no significant difference between their mean scores, it should be noted that the reason for this will be because the sample size is small.
If a large sample size was used, this could have been different as thsi could result in a significant difference between their mean scores.
secA-tanA=(cosA/2-sinA/2)/(cosA/2+sinA/2)
Answers
Answer:
Step-by-step explanation:
SecA - TanA
= 1/CosA - SinA/CosA
= 1 - SinA/CosA
We know that Sin2A = 2SinACosA and Cos2A = Cos²A - Sin²A
Thus SinA = Sin2(A/2) = 2Sin(A/2)CosA/2
CosA = Cos2(A/2) = Cos²A/2 - Sin²A/2
Now substituting the values back,
=> 1 - 2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)
// we know that Sin²θ + Cos²θ = 1
=> Sin²(A/2) + Cos²A/2 - 2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)
//We know that numerator is of form a² + b² - 2ab which is (a - b)².
//Similarly denominator is of form a² - b² which is (a - b)(a + b)
=> [Sin(A/2) - Cos(A/2)]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [ - {Cos(A/2) - Sin(A/2)}]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [Cos(A/2) - Sin(A/2)]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [Cos(A/2) - Sin(A/2)] / [Cos(A/2) + Sin(A/2)]
= R.H.S
Hence proved.
Please help!!!......
Answers
Answer:
12*12=144
8*10=80
80+144=224
224*2=448
10*4=40
8*10=80
80*2=160
40+160=200
12*10=120
120+200=320
20*10=200
320+200=520
448+520=968
Hope This Helps!!!
I WILL GIVE BRAINLIEST IF TWO PEOPLE ANSWER! PLEASE PUT WHAT X IS, AND PLEASE PUT THE REASONS OF HOW YOU DID IT, FOR INSTANCE, SUBSTITUTION, OR ALTERNATE INTERIOR ANGLES
Answers
Answer:
14°
Step-by-step explanation:
4x + 32 + 64 = 180 => x = 14 (°)
HELP! I'LL GIVE BRAINLIEST ! ! ! ! ! ! ! !
Select all of the quadrants that the parabola whose equation is y = √x - 4 (principal square root) occupies.
a. IV b. III c. II d. I
Answers
Quadrants I and IV
When we graph y^2 = x - 4, we see that it is on the x axis, and goes up into Quadrant I, and down into Quadrant IV
rút gọn M=[ căn x -2/x-1- căn x +2/x+2 căn x+ 1] nhân x bình-2x+1/2 với x>0 x khác 1
Answers
Answer:
Step-by-step explanation:
Decide whether the graphs of the two equations are parallel. y=3x+8 and y/3-3=x
Answers
Answer:
Equation #1:
[tex]y = 3x + 8[/tex]
Equation #2:
[tex]\frac{y}{3} -3=x\\\\\frac{y}{3}=x+3\\\\y=3(x+3)\\\\y=3x+9[/tex]
Parallel equations have the same slope. Since both share the same slope of 3, they're parallel.
Solve the equation. Then check your solution.
x - 4 = 2
a.–6
c.7
b.6
d.–2
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
b) 6
Step-by-step explanation:
x - 4 = 2
x = 2 + 4
x = 6
Two cars leave the park at the same time opposite directions one goes 3 times faster after 6 hours they travel 140miles how fast did theyg go
Answers
Answer:
Their speeds are;
5.83 mph and 17.49 mph
Step-by-step explanation:
We are told that they leave the park the same time.
Let the speed one car traveled be v
Since the other car is 3 times faster, then it means that, it's speed is 3v.
Now, after 6 hours they travel 140 miles.
We know that;
Speed = distance/time.
Thus;
(v + 3v) = 140/6
4v = 140/6
v = 140/24
v = 5.83 mph
Thus, second car's speed = 3v = 3 × 5.83 = 17.49 mph
Many track hurdlers believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track hurdlers in the different starting positions. Find the critical value to test the claim that the probabilities of winning are the same in the different positions. Use 0.05. The results are based on 240 wins.
Answers
Answer:
χ² = 6.75
χ² Critical = 11.07
Step-by-step explanation:
Given the data :
Expected winnings ;
1/n * total number of wins
Total number of wins = 240
n = number of starting positions = 6
Expected winnings = 1/6 * 240 = 40
Using χ² test :
χ² = Σ(O - E)² / E
O = Observed ; E = Expected
χ² = (32 - 40)^2 / 40 + (33 - 40)^2 / 40 + (45 - 40)^2 / 40 + (44 - 40)^2 / 40 + (50 - 40)^2 / 40 + (36 - 40)^2 / 40
= 6.75
χ² Critical at α = 0.05 ; df = n - 1 ; df = 5
χ² Critical = 11.07
Since χ² < χ² Critical ; WE fail to reject H0.
-4d - 5 = -1 answer for me pls
Answers
[tex]\\ \sf\longmapsto -4d-5=-1[/tex]
Cancel - from both sides[tex]\\ \sf\longmapsto -(4d+5)=-(1)[/tex]
[tex]\\ \sf\longmapsto 4d+5=1[/tex]
[tex]\\ \sf\longmapsto 4d=1-5[/tex]
[tex]\\ \sf\longmapsto 4d=-4[/tex]
[tex]\\ \sf\longmapsto d=\dfrac{-4}{4}[/tex]
[tex]\\ \sf\longmapsto d=-1[/tex]
By using determinant method solve following questions 3x+4y+5z=18. 2x-y-8z=13. 5x-2y+7z=20
Answers
Answer:
Copied text is stored in the clipboard for 1 hour.
Find the measure of the indicated angle.
Answers
Answer:
i think it the measured of the indicated angle is 55
If the children were to share the juice equally, how much would each child get? Line plot below plz show your work
Answers
Answer:
thanks for your question it is a good question but I need other part of your paper to see 3-7 questions
Step-by-step explanation:
i think there are 8 children in totally
Answer:
2 1/3 quartsStep-by-step explanation:
According to the plot we have
Number of children:
(1 + 3 + 1 + 2 + 1) = 8Total amount of juice:
1*(1 4/6) + 3*(2) + 1*(2 2/6) + 2*(2 5/6) + 1*(3) = 10/6 + 6 + 14/6 + 34/6 + 3 = 58/6 + 9 = 9 4/6 + 9 = 18 2/3 quartsIf shared equally each of the children would get:
18 2/3 : 8 = 56/3 * 1/8 = 7/3 = 2 1/3 quartsAn angle measures 89.8° more than the measure of its complementary angle. What is the measure of each angle?
Answers
Complementary angles always are 90 degrees when added to each other, so:
x = angle 1
x + 89.8 = angle 2
x + x + 89.8 = 90
2x = 90 - 89.8
2x = 0.2
x = 0.1
angle 1 = 0.1 degrees
angle 2 = 0.1 + 89.8 = 89.9 degrees
if you want to check, just sum one to the other and see if they equal 90, like this: 89.9 + 0.1 = 90
In a right triangle ∠A = 32° with an adjacent side of 44 what is the length of the opposite side, x?
Answers
Answer: About 27.49
Step-by-step explanation:
You use the laws of tangent within a triangle to find x:
[tex]tan(32)=\frac{opposite}{adjacent}= \frac{x}{44}\\ \\x=44*tan(32)=27.49425...[/tex]
Which of the following lists of ordered pairs is a function? A. (2,5), (3, 6), (6, 9) B. (-1,2), (2, 3), (3, 1), (2,5) C. (1,2), (4,0), (3,5),(4,3) D. (2,5), (3, 6), (2, 1)
Answers
Answer:
A. (2,5), (3,6), (6,9)
Step-by-step explanation:
In order to be a function, all inputs (x values) must go to only one output (y value). List A is the only list that obeys this rule. Therefore, List A is a function.
a) (x3 – 7x + 3 – x2) : (x – 3);
b) (2x4 – 3x3 – 3x2 – 2 + 6x) : (x2 – 2)
Answers
Answer:
Step-by-step explanation:
X^2+2x-1
2X^2-3x+1
Surveys were sent to a random sample of owners of all-wheel-drive (AWD) vehicles and to a random sample of owners of front-wheel-drive (FWD) vehicles. The proportion of owners who were satisfied with their vehicles was recorded for each sample. The sample proportions were used to construct the 95 percent confidence interval for a difference in population proportions (FWD minus AWD) for satisfied owners. The interval is given as (−0.01,0.12). A car company believes that the proportion of satisfied owners of AWD vehicles differs from the proportion of satisfied owners of FWD vehicles. Does the confidence interval provide evidence that this belief is plausible?
Answers
Answer:
No, the confidence interval does not provide evidence that this belief is plausible as the confidence interval range contains the null value (0)
Step-by-step explanation:
Given that the confidence interval for the mean difference of AWD and FWD vehicles is :
(−0.01,0.12)
When defining the hypothesis for mean difference :
H0 : μ1 - μ2 = 0
H1 : μ1 - μ2 ≠ 0
Using the confidence interval result, reject the Null if the confidence interval value at the given α - level does not contain 0 ; otherwise fail to reject the Null ;
Since the (−0.01,0.12) contains 0 ; then we fail to reject the Null and conclude that there is no statistically significant difference between the two groups
Simplify the Following
4×7-63÷9+20
Answers
Answer:
41
Step-by-step explanation:
pay attention to the order of operation
4*7 - 63/ 9 +20, first multiplication and division from left to right
28 - 7 + 20 , second addition and subtraction from left to right
21 +20
41
Answer:
Step-by-step explanation:
Use PEDMAS
First perform division, then multiplication and then addition & subtraction.
4 * 7 - 63÷9 + 20 = 4*7 - 7 + 20 {Division}
= 28 - 7 + 20 {Multiplication}
= 41
Juan concludes that x? + 7x + 3 cannot be factored using integers.
is juan correct? how could juan improve his strategy?
Answers
I HOPE IT WILL HELP YOU. If it is right then plz tell me .
Can someone please help marking brainliest
Answers
Answer:
down below!
Step-by-step explanation:
a) width: 2,3,4,5 length:9,8,7,6
all you need if for those numbers to add up to 11 together because the perimeter itself is 22 so you always want to be able to add those two numbers and be able to double it to the perimeter if that makes sense.
b) the greatest area there will be would be width: 5 and length: 6 because 5x6 equals 30 and multiplying the others would be less than that. hence 2x9=18, 3x8=24, and 4x7=28
please let me know if this helps if not I can try to explain another way!
