Find the unknown sides and angles of this triangle using the Law of Cosines. Round to the nearest hundredth.
Answers
Step-by-step explanation:
as we know
law of cosine
[tex]c = \sqrt{ {a}^{2} + {b}^{2} - 2ab. \cos(c) } [/tex]
[tex]c = \sqrt{ {14}^{2} + {18}^{2} - 2.14.18 - \cos( {35}^{o} ) } [/tex]
[tex]c = 10.35[/tex]
using the law of cosine
[tex]cos(a) = \frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc} [/tex]
[tex] \cos(a) = \frac{ {18}^{2} + {10.35 }^{2} - {14}^{2} }{2.18.(10.35)} [/tex]
[tex]a = {50.87}^{o} [/tex]
b=87.13°
Related Questions
A 12-meter ladder leans against a building forming a 30° angle with the building.
Exactly how high is the ladder on the building in meters? Round to the nearest hundredth
(2 digits after the decimal).
Answers
Answer:
will show you two (2) ways to solve this problem.
A diagram is needed to see what is going on....
Without loss of generality (WLOG)
The wall is on the right. The ladder leans against the wall
with a POSITIVE slope, from SW to NE (quadrant 3 to quadrant 1).
The measure from the bottom of the ladder to the wall is 6.
Option 1:
The ladder, ground and wall form a right triangle.
The hypotenuse (ladder) is 14 feet.
The bottom of the ladder is 6 feet from the wall,
so the base of this right triangle is 6 feet.
The top of the ladder to the ground represents
the missing leg of the right triangle.
The pythagorean theorem applies, which says
6^2 + h^2 = 14^2 where h is the height
of the top of the ladder to the ground
36 + h^2 = 196
h^2 = 196 - 36
h^2 = 160
h = sqrt(160)
= sqrt(16 * 10)
= sqrt(16)* sqrt(10)
= 4*sqrt(10) <--- exact answer
= 4 * 3.16227766016838....
= 12.64911....
12.65 <--- rounded to 2 digits as directed
----------------------------------------------
Option #2: using trig
With respect to the angle formed by the bottom of the
ladder with the ground
cos T = 6/14 = 3/7
T = inverse-cosine(3/7) = 64.623006647 degrees
sin(64.623006647) = h/14
h = 14*sin(64.62300647) = 12.6491106 <--- same answer
hope this helps
Step-by-step explanation:
Please help me
Which equation below best represents the relationship between corresponding values in the table above?
Answers
Answer:
D
Step-by-step explanation:
Answer:
Its D
Step-by-step explanation:
I was to lazy to provide an explanation
What is the slope for y= -8x + 3
A) -8
B) -5
C) 3
D) 8
Answers
PLEASE HELP ME!!!! I’ll give Brainiest
Answers
Answer:
y=1/3x+2
do (6,0) and (0,2)
Step-by-step explanation:
josefina pain rent for 5 months. She paid a total of $2045. how much did she pay per month?
Answers
Answer:
$409 per month
Step-by-step explanation:
If josefina paid $2045 over a time period of 5 months, then we have to divide how much she paid ($2045) by 5 to find out how much she paid for rent in 1 month.
We can use the equation: 2045 ÷ 5
When we solve that equation, we get 409 which means that josefina paid $409 per month for rent.
(sorry if this is confusing but I hope it helped)
An 8th grade class project involves decorating a rectangular box with the following dimensions.
length: 12 inches
width:834 inches
height:1012 inches
What is the total surface area of this box to the nearest hundredth?
Answers
Answer:1500
Step-by-step explanation: so i got the anwser 1539.2 and just rounded to the nearest hundredth which is 1500 hopefully it helps!
Students who attend Anytown College pay either in-state or out-of-state tuition, depending on where they reside. The amount, I, spent on in-state tuition for a randomly selected student has a mean of $2,523.75 and a standard deviation of $1,003.25. The amount, O, spent on out-of-state tuition for a randomly selected student has a mean of $3,825.00 and a standard deviation of $1,126.50.
Suppose we randomly select one student who pays in-state tuition and one student who pays out-of-state tuition.
Calculate the mean of the sum S = I + O.
μS = $227.69
μS = $1,301.25
μS = $1,508.48
μS = $6,348.75
Answers
Answer:
6,348.75
Step-by-step explanation:
Just add the means. It’s right, just did it!
Using statistical concepts, it is found that the mean of the sum S = I + O is of:
[tex]\mu_S = 6348.75[/tex]
What happens when two variables are added?When two variables are added, the mean is the sum of the means, while the standard deviation is the square root of the sum of the variances.In this problem:
The mean of I is of [tex]\mu_I = 2523.75[/tex].The mean of O is of [tex]\mu_O = 3825.00[/tex].S is the sum of I and O, hence:
[tex]\mu_S = \mu_I + \mu_O = 2523.75 + 3825.00 = 6348.75[/tex]
You can learn more about operations with variables at https://brainly.com/question/26156502
Grace cut 3 pieces of ribbon; each piece was 25 of a foot long. How many feet of ribbon does she have in all? Express your answer as a mixed number
Answers
Answer:
1 1/5
Step-by-step explanation:
3 x 2/5 = 6/5 = 1 1/5
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
Answers
Answer:
A. and D.
Step-by-step explanation:
calmi goes scuba diving she descends 18-ft in 3 minutes which expression represents the average rate at which cami position changes in feet per minute
Answers
jenny is 12 years older than Steve. five years ago, Jenny was four times older than steve was then. how old are each of them now
Answers
Answer:
Jenny 21 years old and Steve 9 years old
What is the perimeter of the triangle, the left diagonal side is 6.1in, the right diagonal side is also 6.1in, the bottom line is 7in, and there is a line in the middle from top to bottom which is 5in. What is the perimeter of the triangle?
Answers
Answer:
19.2 inches
Step-by-step explanation:
6.1 + 6.1 + 7 = 12.2 + 7 = 19.2
perimeter is the outside distance of the shape so you don't need to know the altitude (or height) equals 5.
1
Find the value of the variables.
b
30°
a
12
60°
a-
b =
Answers
Answer:
a=6
b=10.39
Step-by-step explanation:
a=sin 30x12 or a=cos60x12
a=6
b=cos 30x12 or b=sin60x12
b=10.39
I dont really understand it HELP :/
Answers
Answer:
help
/hɛlp/
Learn to pronounce
verb
1.
make it easier or possible for (someone) to do something by offering one's services or resources.
"they helped her with domestic chores"
Similar:
assist
aid
help out
lend a hand to
lend a helping hand to
give assistance to
come to the aid of
succour
aid and abet
be of service to
be of use to
be useful to
do someone a favour
do someone a service
do someone a good turn
bail/bale someone out
come to someone's rescue
give someone a leg up
cooperate with
do one's bit for
rally round
pitch in
chip in
save someone's bacon
save someone's skin
muck in with
get stuck in with
Opposite:
hinder
2.
serve someone with (food or drink).
"may I help you to some more meat?"
noun
the action of helping someone to do something.
"I asked for help from my neighbours"
Similar:
assistance
aid
a helping hand
support
succour
advice
guidance
solution
benefit
use
advantage
service
comfort
avail
cooperation
collaboration
backing
encouragement
a shot in the arm
Opposite:
hindrance
exclamation
used as an appeal for urgent assistance.
"Help! I'm drowning!"
Definitions from Oxford Languages
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Translations and more definitions
People also ask
What is a fancy word for help?
Step-by-step explanation:
What is the solution to -32 + x = 53 ?
Answers
Answer:
positive 85
Step-by-step explanation:
Solve 3x + 4(x + 6) = 45.
Answers
Answer:
x=3
Step-by-step explanation:
3x + 4(x + 6) = 45
Distribute
3x+4x+24 = 45
Combine like terms
7x+24 = 45
Subtract 24 from each side
7x+24-24 = 45-24
7x = 21
Divide each side by 7
7x/7 = 21/7
x=3
Answer:
x =3
Step-by-step explanation:
What expression is equivalent to 5/6 divided by 7
Answers
Answer:
5/42
Step-by-step explanation:
I need to find the postulate
Answers
Jacob walks 1.5 miles north. He turns and walks 0.8 miles west. How far is he from his starting point?
Answers
Answer:
1.7 miles
Step-by-step explanation:
Given that,
Jacob walks 1.5 miles north.
He turns and walks 0.8 miles west.
We need to find how far is he from his starting point. Let he is at a distance of x miles from the starting point. It can be calculated as follows :
[tex]x=\sqrt{1.5^2+0.8^2} \\\\x=1.7\ \text{miles}[/tex]
Hence, he is 1.7 miles from his starting point.
Shreya's Bikes rents bikes for $15 plus $4
per hour. Kali paid $47 to rent a bike. For
how many hours did she rent the bike?
A) 8 B) 7
C) 11.75 D 9
Answers
Answer:
A, 8
Step-by-step explanation:
Use the equation 15+4x=47
Subtract 15 from both sides to get
4x=32
divide to get 8
x=8
Rectangle ABCD was dilated to create rectangle A'B'C'D. Triangle A B C D is dilated to form triangle A prime B prime C prime D. Side B C is 3.8 units. Side A prime B prime is 15 units and side B prime C prime is 9.5 units. What is AB? 6 units 7.6 units 9.5 units 12 units
Answers
Answer:
[tex]AB = 6[/tex]
Step-by-step explanation:
Given
[tex]BC = 3.8[/tex]
[tex]A'B' = 15[/tex]
[tex]B'C' = 9.5[/tex]
Required
Determine the length of AB
Because A'B'C'D is a dilation of ABCD, then the following relationship must exist:
[tex]A'B' : AB = B'C' : BC[/tex]
Substitute values for A'B', B'C' and BC
[tex]15 : AB = 9.5 : 3.8[/tex]
Express the ratio as fractions:
[tex]\frac{AB}{15} = \frac{3.8}{9.5}[/tex]
Multiply through by 14
[tex]15 * \frac{AB}{15} = \frac{3.8}{9.5} * 15[/tex]
[tex]AB = \frac{3.8}{9.5} * 15[/tex]
[tex]AB = \frac{3.8* 15}{9.5}[/tex]
[tex]AB = \frac{57}{9.5}[/tex]
[tex]AB = 6[/tex]
Answer:
A. 6 units
Step-by-step explanation:
I got it right on edge.
help me out I’m confused.
Answers
Answer:
33
Step-by-step explanation:
55²- 44²= 1089
square root of 1089 = 33
Segment AB falls on line 6x + 3y = 12. Segment CD falls on line 4x + 2y = 8. What is true about segments AB and CD? They are parallel because they have the same slope of −2. They are parallel because they have the same slope of one half. They are lines that lie exactly on top of one another because they have the same slope and the same y-intercept. They are lines that lie exactly on top of one another because they have the same slope and a different y-intercept.
Answers
The lines 6x + 3y = 12 and 4x + 2y = 8 lie exactly on top of one another because they have same slope and same y intercept.
What are the coincident lines?The lines which coincide or lie on the top of each other are called coincident lines.
When the two lines coincide to each other?Two lines coincide to each other when they have same slope and same y intercept.
According to the given question.
We have two equation of lines.
[tex]6x + 3y = 12...(i)[/tex]
And, [tex]4x + 2y = 8...(ii)[/tex]
The equation (i) can be written as
[tex]2x + y = 4[/tex]
And equation (ii) can be written as
[tex]2x + y = 4[/tex]
Since, both the lines have same slope and same y intercept. Therefore, the given two lines coincide to each other.
Hence, the lines 6x + 3y = 12 and 4x + 2y = 8 lie exactly on top of one another because they have same slope and same y intercept.
Find out more information about coincident lines here:
https://brainly.com/question/18496998
#SPJ2
John buys a Seahawks beanie that cost $18, but is on sale for 20% off. Jane
buys a Seahawk scarf that costs$25, but is on sale for 25% off. Find the
difference in the amount John and Jane paid, after the discounts. Write
and solve proportions to find the answer, round your answer to the nearest
cent, and include units. *
Answers
Answer:
18/100 X 80 =14.40
25/100 X 75 =18.75
18.75 - 14.40 = 4.35
Due asap
Show workings please
Answers
Answer:
x= 11.4° (1 d.p.)
Step-by-step explanation:
Please see the attached picture for the full solution.
Find the value of x in the triangle. SU RV
Answers
Answer:
x = 8
Step-by-step explanation:
Δ TSU and Δ TRV are similar , thus the ratios of corresponding sides are equal, that is
[tex]\frac{TS}{TR}[/tex] = [tex]\frac{TU}{TV}[/tex] , substitute values
[tex]\frac{x}{x+16}[/tex] = [tex]\frac{5}{15}[/tex] = [tex]\frac{1}{3}[/tex] ( cross- multiply )
3x = x + 16 ( subtract x from both sides )
2x = 16 ( divide both sides by 2 )
x = 8
write the equation for the parabola that has x-intercepts (2,0) and (3,0) and y intercept (0,-1.2)
Answers
Answer:
i think its y=-0.2x^2+x-1.2
Step-by-step explanation:
i could be wrong tho ngl
The equation of the parabola with x-intercepts (2,0) and (3,0) and y-intercept (0,-1.2) will be y = (-1/5)(x - 2)(x - 3).
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
The graph is easy to understand the behavior of the graph.
For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.
The equation of a parabola is written as,
y = a(x - b)(x - c) here b and c are two x-intercepts while (a,y) is the y-intercept.
As per the given,
x-intercept = (2,0) and (3,0)
y-intercept = (0,-1.2)
y = a(x - 2)(x - 3)
-1.2 = a(0 - 2(0 - 3)
a = -1/5
Thus,
y = (-1/5)(x - 2)(x - 3)
Hence "The equation of the parabola with x-intercepts (2,0) and (3,0) and y-intercept (0,-1.2) will be y = (-1/5)(x - 2)(x - 3)".
To learn more about graphs,
brainly.com/question/16608196
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You plan to purchase a plane ticket for $299.00 and you are going to use a discount code to
receive 15% off. How much will the ticket cost AFTER the discount?
Answers
Answer:
$44.85
Step-by-step explanation:
15/100 * $299.00= $44.85
!!!! Help please whoever evaluates it I’ll give you Brainly
Answers
Answer:
733
Step-by-step explanation:
3*3 =9
3*3=9
3*3=9
9*9= 81*9= 729+4 = 733
Jen used 1/2 cup of cereal and 2/3 cup of nuts to make trail mix. Her mother asked if she used more cereal or more nuts in the mix. Which statement correctly compares the fractions?
Answers
1/2<2/3. 1/2= half of a whole and half of a whole is 1/2. 2/3 is over a half so it means that 2/3 is better then 1/2 since 1.5 is actually the half of 3. Jen should say that she used more nuts to make trail mix then using cup of cereal to make trail mix because 2/3 is greater then 1/2.
