Question

Type the correct answer in each box. Round your answers to the nearest tenth.
A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground.
The angle made by the ladder with the ground is blank
degrees, and the length of the ladder is blank
inches.

Answer 1

Draw a diagram  (see attachment)

we can find the length of the ladder first using pythagorean theorem then use cos⁻¹(x) to find the angle measure

or

we can use tan⁻¹(x) to find the angle measure then use cos(x) to find the hyptotonuse

I'll use the first way

alrighty, so we can find the hypotnuse by using pythagoreano therrem which can be used for right triangles

so if legs are a and b and hytponuse is c then

a²+b²=c²

so

legs are 30 and 50

30²+50²=c²

900+2500=c²

3400=c²

sqrt both sides

10√34=c

the length of the ladder is 10√34 in

ok, so we know hyptonuse is 10√34

cos=adjacent/hypotonuse

but we can use cos⁻¹(x)

cos⁻¹(30/(10√34))=x°

use your calculator

59.03≈x°

the degree measure is about 59° and the length of the ladder is 10√34 in or about 59.3in