part 2. Find the value of the trig function indicated, use for that Pythagorean theorem to find the third side if you need it.
Answers
Answer: [tex]\bold{5)\ \cos \theta=\dfrac{\sqrt{11}}{6}\qquad 6)\ \tan \theta =\dfrac{8}{17}\qquad 7)\ \cos \theta = \dfrac{4}{3}\qquad 8)\ \cos \theta = \dfrac{\sqrt{10}}{10}}[/tex]
Step-by-Step Explanation:
Pythagorean Theorem is: a² + b² = c² , where "c" is the hypotenuse
[tex]5)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3\sqrt{11}}{18}\quad \rightarrow \large\boxed{\dfrac{\sqrt{11}}{6}}[/tex]
Note: (15)² + (3√11)² = hypotenuse² → hypotenuse = 18
[tex]6)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{8}{17}\quad =\large\boxed{\dfrac{8}{17}}[/tex]
Note: 8² + 15² = hypotenuse² → hypotenuse = 17
[tex]7)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{20}{15}\quad \rightarrow \large\boxed{\dfrac{4}{3}}[/tex]
Note: hypotenuse not needed for tan
[tex]8)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{2}{2\sqrt{10}}\quad =\large\boxed{\dfrac{\sqrt{10}}{10}}[/tex]
Note: 2² + 6² = hypotenuse² → hypotenuse = 2√10
5) cosθ = [tex]\frac{\sqrt{11} }{6}[/tex] , 6) cosθ = [tex]\frac{8}{17}[/tex] , 7) tanθ = [tex]\frac{4}{3}[/tex] , 8) cosθ = [tex]\frac{1}{\sqrt{10} }[/tex]
What is pythagorean theorem ?If, a be the perpendicular, b be the base & c be the hypotenuse of a right angle triangle.
Then, [tex]c=\sqrt{a^{2}+ b^{2} }[/tex]
What are the trigonometric functions ?cosθ = (Side adjacent to θ)/(Hypotenuse)
sinθ = (Side opposite to θ)/(Hypotenuse)
tanθ = (Side opposite to θ)/(Side adjacent to θ)
What are the values of required trigonometric functions ?5) Hypotenuse = [tex]\sqrt{(3\sqrt{11}) ^{2} +15^{2} }[/tex]
= [tex]\sqrt{99+225}[/tex]
= [tex]\sqrt{324}[/tex] = 18
∴ cosθ = (Side adjacent to θ)/(Hypotenuse)
= [tex]\frac{3\sqrt{11} }{18}[/tex] =[tex]\frac{\sqrt{11} }{6}[/tex]
6) Hypotenuse = [tex]\sqrt{8^{2} +15^{2} }[/tex]
= [tex]\sqrt{64+225}[/tex]
= [tex]\sqrt{289}[/tex] = 17
∴ cosθ = (Side adjacent to θ)/(Hypotenuse)
= [tex]\frac{8}{17}[/tex]
7) tanθ = (Side opposite to θ)/(Side adjacent to θ)
= [tex]\frac{20}{15}[/tex] = [tex]\frac{4}{3}[/tex]
8) Hypotenuse = [tex]\sqrt{2^{2} +6^{2} }[/tex]
= [tex]\sqrt{4+36}[/tex]
= [tex]\sqrt{40}[/tex] = [tex]2\sqrt{10}[/tex]
∴ cosθ = (Side adjacent to θ)/(Hypotenuse)
= [tex]\frac{2}{2\sqrt{10} }[/tex] = [tex]\frac{1}{\sqrt{10} }[/tex]
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Related Questions
What is the volume of the sphere shown below?
--12-
A. 5767 units 3
B. 691277 units3
C. 23041 units
O D. 19271 units3
Answers
Answer:
answer is B
Step-by-step explanation:
Volume of the sphere is 2.304[tex]\pi[/tex] unit³ or 7234.56 unit³.
What is a sphere ?A sphere is a three dimensional solid shape. It is a set of points that are all at the same distance r from a common point. The distance r is the radius and the common point is the centre of the sphere.
Here,
The radius of the sphere is given by,
r = 12 units
The equation for volume of a sphere with radius r is given by,
V = 4/3 [tex]\pi[/tex]r³
So, the volume of the sphere is,
V = 4/3 x [tex]\pi[/tex] x 12³
V = 2.304 [tex]\pi[/tex]
V = 7234.56 unit³
Hence,
Volume of the sphere is 2.304[tex]\pi[/tex] unit³ or 7234.56 unit³.
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I can’t tell if my answer is correct , please help !!!!!! Will mark brainliest !!!!!!!!!!!!
Answers
Answer:
You should be right
Step-by-step explanation:
Srry if I am wrong though
Identify the diameter if given the radius and the radius if given the diameter of given circles: 7 cm 25 cm 28 cm 35 cm 100 cm 140 cm Radius = 70 cm Radius = 14 cm Diameter = 14 cm Diameter = 50 cm Radius = 70 cm Radius = 14 cm Diameter = 14 cm Diameter = 50 cm
Answers
Answer:
Radius. 7, 25, 14, 35, 50, 70
Diameter 14, 50, 28, 70, 100, 140
Which of the following statements uses the commutative property of addition
2+(3+4)=(2+3)+4
2+(3+4)=(2+3)+(2+4)
2+(3+4)=2+(4+3)
Answers
Answer:
the first one
Step-by-step explanation:
The second equation doesn't make sense because that's not a true statement. The third equation uses the associative property so the answer must be the first one.
what are the domain and range of the function on the graph
Answers
which of the following is a solution of y > |x| -5?
A.(-4,1)
B.(-1,-4)
C.(4,-1)
Answers
Answer:
the answer is A. (-4,1)
Step-by-step explanation:
because the point is inside of the shades area of the function. meaning is including the value. the other two points are in the dotted line meaning is not included
Which side of XYZ is the longest?
262
63
X
A. XY
B. XZ
C. YZ
o
D. Cannot be determined
Answers
Answer:
A. XY
Step-by-step explanation:
XY because it's opposite to the greatest angle.
Answer:
A.XY
Step-by-step explanation:
Sandy wants to make a punch recipe with 2 parts pineapple juice to 6 parts ginger ale if you wants to increase the recipe using a parts pineapple juice,
How much ginger-ale should she use?
18
28
(24
Answers
Answer:
24
Step-by-step explanation:
If you go from 2 parts pineapple to 8, thats a 4x increase. Therefore 6x4=24 (6 from the Ginger)
A student says that 5x2=20, then x must be equal to 2. Do you agree or disagree with the student? Justify your answer.
Answers
Answer:
Step-by-step explanation:
I disagree. If each side of the equation is divided by 5, the result is x2 = 4. By the square root property of equality, x = -2 or x = 2. So x could be -2 instead of 2.
Answer:
I disagree. If each side of the equation is divided by 5, the result is x2 = 4. By the square root property of equality, x = -2 or x = 2. So x could be -2 instead of 2.
Step-by-step explanation:
solve for x.
12x - 8 = 8x - 20
Answers
Answer:
x= -3
Step-by-step explanation:
12x-8x = -20+8
4x = -12
x= -12/4
x = -3
Steps:
Step 1: Subtract 8x from both sides.
12x−8−8x=8x−20−8x
4x−8=−20
Step 2: Add 8 to both sides.
4x−8+8=−20+8
4x=−12
Step 3: Divide both sides by 4.
4x/4 = −12/4
Answer: x=−3
Please mark Brainliest
Hope this helps.
Express 0.96 as an percent
Answers
Answer:
96%
Step-by-step explanation:
0.96 × 100/100
(0.96 × 100)× 1/100 = 96/100
percentage = 96%
Answer:
96%
Step-by-step explanation:
Use the quadratic formula to solve the equation. 9x2−7x+1=0 Enter your answers, in simplified radical form. x = x =
Answers
Answer:
[tex]x=\frac{\sqrt{13}-7 }{18} ,x=\frac{-\sqrt{13}-7 }{18}[/tex]
Step-by-step explanation:
I'm not too good with the quadratic formula so I'm going to complete the square.
First divide everything by 9 and move the 1 to the other side.
[tex]x^2-\frac{7}{9}=-\frac{1}{9}[/tex]
Then take half of [tex]\frac{7}{9}[/tex] and square it and add it to both sides.
[tex]x^2-\frac{7}{9} +\frac{49}{324}=\frac{13}{324}[/tex]
Now you can factor it.
[tex](x-\frac{7}{18})^2=\frac{13}{324}[/tex]
Square root:
[tex]x-\frac{7}{18}=\frac{\sqrt{13} }{18}[/tex]
[tex]x=\frac{\sqrt{13}-7 }{18} ,x=\frac{-\sqrt{13}-7 }{18}[/tex]
The polynomial f(x) is written in factored form: f(x) = (x − 3)(x + 8)(x − 11) What are the zeros of the polynomial function?
x = 3, x = 8, x = 11
x = 3, x = −8, x = 11
x = −3, x = 8, x = −11
x = −3, x = 3, x = −8, x = 8, x = −11, x = 11
Answers
Answer:
x=3 x = -8 x = 11
Step-by-step explanation:
f(x) = (x − 3)(x + 8)(x − 11)
Using the zero product property
0 = (x − 3)(x + 8)(x − 11)
0 = x-3 0 = x+8 0 = x-11
x=3 x = -8 x = 11
Answer:
x=3 x = -8 x = 11
Hope this helps!
Find the slope and the y-intercept of the graph of the linear equation. y = −7x + 2 *
Answers
Answer:
slope = - 7, y- intercept = 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 7x + 2 ← is in slope- intercept form
with slope m = - 7 and y- intercept c = 2
Someone have the answer please ?!
Answers
True if the lines were not vertical this would be false.
M(angle)1 =. Degrees
Answers
Answer:
Angle [tex]m\angle 1 = 35^o[/tex]
Step-by-step explanation:
Our goal is to find appropriate symmetries within the given diagram, so we can use the property of the addition of internal angles of a triangle that render [tex]180^o[/tex].
So we start by drawing a line that goes through the center of the circle and also through the vertex of angle [tex]m\angle 1[/tex]. Please see the attached image to follow the procedure. In the image, the line is a fine black line that crosses the circle completely.
Now we draw the four radii that will define clearly the central angles of [tex]100^o[/tex] and [tex]30^o[/tex] that come as information.
Then we set our efforts to analyze the two triangles (one marked with green borders, and the other one marked with orange borders. Notice that the angle on the further right for the triangle with orange borders is in fact half of the angle [tex]m\angle 1[/tex] that we need to find, so we will work our way to determine the size of it and then multiply it by two.
We need to start though with the triangle with green borders because it has more information that we can derive.
Notice that this green triangle has a central angle equal to [tex]115^o[/tex], because it has to measure the same as 180 degrees minus half of the 100 degrees angle and minus half of the 30 degree angle in order to add to form the perfect plane angle of the circle's diameter:
[tex]180^o-50^o-15^o=115^o[/tex]
Now, notice as well that this green triangle is an isosceles triangle (has two equal sides (both equal to the radius of the circle), and therefore the angles opposite to them must be equal. We can find the measure of either such angles by using the property of additions of internal angles of a triangle to render [tex]180^o[/tex], subtracting from it the 115 degree angle we know, and dividing the result by two:
[tex]180^o-115^o=65^o[/tex]
half of this is [tex]32.5^o[/tex]
Now we use this angle, to find its supplementary angle, which would be the angle on top of the orange triangle:
[tex]180^o-32.5^o=147.5^o[/tex]
Now all we need is to use the property of addition of internal angles for the orange triangle (of which we currently know a 15 degree angle and a 147.5 degree angle) to find what half of angle [tex]m\angle 1[/tex] is:
[tex]180^o-147.5^o-15^o=17.5^o[/tex]
then angle [tex]m\angle 1[/tex] is twice this value: [tex]m\angle 1 = 35^o[/tex]
if james is 9years old and his sister rose is 15 years . what is the sum of their ages
Answers
Answer:
24 years
Step-by-step explanation:
James Age = 9 years
Rose's Age = 15 years
Sum of their Ages = 9+15
Sum of their Ages = 24 years
There are three people in lee’s family. The range if their shoe sizes are 3. Two people in her family wear size 6. Lee’s size is not 6 or 3. What is Lee’s shoe size?
Answers
Answer:
I would say 9
Step-by-step explanation:
range is the difference between the largest and the smallest values in a data set. the range in this case is 3. so, we have to either add to 6 or subtract from 6.
but we've been told that Lee's shoe size is not three so it 6 + 3 = 9.
hope this helps
if 4a + 6 = 12 - 2a what is 6a
Answers
___________________________
Hey!!
Solution
4a+6=12-2a
or,4a+2a=12-6
or,6a=6
or,a=6/6
a=1
The value of a is 1.
hope it helps...
Good luck on your assignment
_________________________
value of 6a = 6* 1 = 6
What is linear equation ?
In a linear equation coefficients can be positive or negative values and in which the highest power of the variable is always 1 .
according to question the linear equation given is :
4a + 6 = 12 - 2a
find = 6a ?
4a + 6 = 12 - 2a
6a = 12 - 6
6a = 6
a = 1
since , substituting value of a
6a = 6* 1 = 6
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salim had 24 homework problems he completed 12 problems during lunch then he completed 7 more after school
Answers
Answer:
So how many he has left to do???
I think Salim has to finish 5 more problems
Step-by-step explanation:
Please I need help
With this question thank you for your help me
Answers
Answer:
Using CPCTC we can derive that WM = 8 and OL = 10.
What is the product?
(-35 +21)(45-1)
Answers
Answer:
-616
Step-by-step explanation:
First subtract 35 with 21 since 35 is a negative. then subtract 45 with 1
for the first parenthesis would be -14. the second parenthesis would be 44.
then multiply both of the answers together to get -616
Answer:-220
Step-by-step explanation:
Which of these is an equation? 8t+4=76 8t+4 8z 8+4
Answers
Answer:
8t+4=76
Step-by-step explanation:
An equation needs an equals sign otherwise it is an expression
Seventy of Myra’s classmates are traveling by bus to a football game in another town. They hired 2 buses, but there were only 64 seats. The remaining 6 students had to travel in a separate van.
The equation 2b + 6 = 70 represents the given scenario. What does b represent?
Answers
Answer:
32
Step-by-step explanation:
2b+6=70
-6=70-6=64
[tex]\frac{2b}{2}[/tex]=64÷ 2
b=32
beaten it's a visable line beween the equal line
what is being constructed based on the markings in the following diagram???
Answers
Answer:
What diagram though?
'
Step-by-step explanation:
If p(x) = x + 3, then p(x) + p(–x) is equal to ??
Answers
Answer:
The answer is 6
Step-by-step explanation:
p(x) = x + 3
p(-x) = -x + 3
=> p(x) + p(-x) = x + 3 + (-x) + 3 = 6
Hope this helps!
:)
The following are the ages (years) of 5 people in a room: 15, 17, 22, 14, 19 A person enters the room. The mean age of the 6 people is now 19. What is the age of the person who entered the room?
Answers
Answer:
27
Step-by-step explanation:
Given that:
(15+17+22+14+19+x) divided by 6 = 19
(87 + x) divided by 6 = 19
87 +x = 114
so x = 27.
Therefore the age of person 6 = 27
What whole number does: 20/5represent?
Answers
Answer:
4
Step-by-step explanation:
20/5 = 4
Answer:
4
Step-by-step explanation:
cause 20/5 is 4 meaning it represents 4
Nearest hundredth
X2+2x+7=21
Answers
Step-by-step explanation:
subtract 21 from both sides
x2+2x+7-21=21-21
x2+2x+14=0
use quadratic equation
x=(-3+-(b^2-4ac)^1/2)/2a
in our equation a=1,b=2and c=14
(-2+-(14+56)^1/2)/2
x=-1+(60^1/2)/2
there is only one positive answer and it is 2.87
I need help ASAP I shall give brainlyist (idk how to spell it)
Answers
Answer:
3014.4ft³
Step-by-step explanation:
V=Πr²h(volume of cylinder)
=(3.14)(8)²(15)
=3014.4ft³
