Question

I have a math question if anybody can help :)!! thnx

Answer 1

A ladder leans against a house at a 60° angle to the ground.



If the ladder extends to a length of 158 inches, what is the height of the house rounded to the nearest hundredth of an inch? Type the numeric answer only in the box below.

Answer 2

You could use this property of the 30-60-90 triangle:
Its sides have proportions \(a : a \sqrt{3} : 2a\), going from the shortes to the longest.

Answer 3

okay but how would I plug that in??

Answer 4

use the sine formula

sin(theta) = opposite side/ hypotenuse.

in your case theta is 60 degrees
the opposite side is x
what is the hypotenuse.

Answer 5

ummmm....158?

Answer 6

You can plug it in this way: FG = 158 = 2a, so a = 79 (=EF)
The height of the house is x = 79√3.
Calculator says: 136.83 inches.

Answer 7

okay...a little confused..but thank you for your help :)

Answer 8

YW!
Here is a drawing of this 30-60-90 triangle, together with the proportions.

Answer 9

thank you so much!!

Answer 10

Important thing to remember here is: if you have the 30-60-90 triangle, you only need ONE side to be able to work out the other two sides.

Answer 11

OKAY I will remember that :) thank you!!

Answer 12

Reason for a and 2a is simple: you can consider the 30-60-90 triangle as a half equilateral triangle.
The a√3 follows from good old Pythagoras.

Answer 13

okay thanks again :) and you have a good day (:

Answer 14

YW! I'll stop now :D

Answer 15

haha lol :) you were helpful!!