Question

A ladder leans against a house at a 60° angle to the ground.
If the ladder extends to a length of 166 inches, what is the height of the house rounded to the nearest hundredth of an inch? Type the numeric answer.

Answer 1

You have a triangle, so you need to use trigonometry.

What function relates the opposite side of x, with the triangle's hypotenuse? The sine function.

So, we take the sine of x: sin(x) = h / 166, where h is the height of the house.

x is given to be 60 degrees, or pi/3 radians.

The sine of pi/3 is sqrt(3)/2.

So we have sqrt(3) / 2 = h / 166. Solving for h:

83 sqrt(3) = h.

Answer 2

Although memorization is not the correct way to learn math, if you memorize the common angles: pi/6, pi/4, pi/4, pi/2, and the standard trig functions at each of those angles, your career in math will be much easier -- since those angles pop up a lot.

Answer 3

Oops, I listed pi/4 above twice.
pi/3 should be included among those.

Answer 4

You are looking for the length of x, and are given 60 degrees and the hypotenuse.

You use the sin function.

sin = opposite / hypotenuse
sin(60 degrees) = x/166

x = 166(sin 20 degrees)

x = 83*sqrt(3) inches = 143.7602 inches -> 144.8 inches

Answer 5

*144.8 inches

Answer 6

143.76 is what I got, but I wasn't sure-thanks!!
Could you help me on another one

Answer 7

sure

Answer 8

Great!
There are many ropes keeping a hot air balloon from floating away before a balloon race. One of these ropes is fixed to the ground at a 45° angle. Another is fixed to the ground at a 30° angle.

If the hot air balloon is 18 feet off the ground, what is the distance between the ground directly underneath the balloon and the second rope rounded to the nearest hundredth of a foot? Type the numeric answer in the box below.
(Picture included)

Answer 9

The distance between the hot air balloon and rope 2 is x, so lets label the distance between the hot air balloon and rope 1 as y. Lets also label the distance between ropes 1 and 2 as z.

In this case: x = y+z

Answer 10

First lets find out the distance of y.

You are given the opposite side and angle, while wanting to find the adjacent side....so you use tangent.

tan(45 degrees) = opposite/adjacent
tan(45 degrees) = 18/y
y(tan 45 degrees) = 18
y = 18/tan 45 degrees

y = 18

Answer 11

Now lets find z

In this case, the opposite side is hypotenuse for triangle 1

Find the hypotenuse:

c^2 = a^2+b^2
c^2 = 18^2+18^2
c^2 = 648
c = 18*sqrt(2)

Answer 12

To find z, we use tangent just as before.

tan(30 degrees) = sqrt(648)/z
sqrt(648) = z(tan 30 degrees)

z = 44.09

x = y + z

x = 18+44.09

x = 62.09 feet

Answer 13

So for this question : "If the hot air balloon is 18 feet off the ground, what is the distance between the ground directly underneath the balloon and the second rope rounded to the nearest hundredth of a foot?"
my final answer is 62.09 ?

Answer 14

Yes, but I haven't done it in a while, but I think that is it

Answer 15

We found the distance between the hot air balloon and rope 2 (x)
the distance between the hot air balloon and rope 1 is y
the distance between the two ropes is z

Answer 16

Thanks .
Can you check the following for me ?

Question: In the figure below, the length of line segment CB is 58 units and the length of line segment BG is 120 units. What is the length of line segment GE?
I got 62 sqroot 3 or option A. as my final answer.

The answers are:
A. 62 square root 3 -> This is what I got , is it correct?
B. 116
C. 58 sqroot 2
D. 124

Answer 17

If BAG = 120, then AG = 120 - BA

Lets say BA = x
Lets say AG = y

First find x.

Answer 18

x:

tan(45 degrees) = 58/x
58 = x(tan 45 degrees)
x = 58

120 - 58 = y = AG = 62

Lets say GE = z

tan(60 degrees) = z/62
x = 62sqrt(3)

Answer 19

You didn't get 62 sqrt 2? :/

Answer 20

The answer choice is 62 root 3, which is what you said you picked

Answer 21

tan(60 degrees) = z/62
z = 62(tan 60 degrees)
z = 107.4 = 62*sqrt(3)

Answer 22

I'm going to close this question discussion and open a new one. Can you join me in the new one?

Answer 23

sure, but isn't that the answer you picked? ...Because you got it right

Answer 24

You're right, just I was looking at another problem, my bad.

Answer 25

ok then.

Sorry for being slow, it's hard to do this on the cpu, but good job. It is a tough problem

Answer 26

Thanks and thank you for your help-no you're not slow. Let me make a new open question and you can join me on a new clean forum .