Question

A 34-ft. ladder resting against the wall of a building forms a right triangle with the wall and ground. The bottom of the ladder is 8 ft. away from the base of the building. How far up the side of the building does this ladder reach? T4L

Answer 1

The ladder resting against the house forms a triangle similar to the one in the image below

To answer this question you must use Pythagorean theorem

$a^{2} +b^{2}=c^{2}$

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = x

b = 8

c =  34

^^^Plug these numbers into the theorem

$x^{2} +8^{2} =34^{2}$

solve for x

$x^{2}$ + 64 = 1156

Subtract 64 to both sides

$x^{2}$ = 1092

Take the square root of both sides

x = √1092

This can be simplified to:

2√273

or

x ≈ 33.045...

The ladder reached roughly 33.05 ft up the wall of the building

Hope this helped!

~Just a girl in love with Shawn Mendes