Question

A painter is placing a ladder to reach the third story window, which is 35 feet above the ground and makes an angle with the ground of 70°.
How far out from the building does the base of the ladder need to be positioned? Round your answer to the nearest tenth.

Answer 1

Answer: the ladder should be placed 12.7 ft from the base of the building.

Step-by-step explanation:

The ladder forms a right angle triangle with the building and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the third story window to the base of the building represents the opposite side of the right angle triangle.

The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.

To determine how far from the base of building that the base of the ladder need to be positioned, h, we would apply the tangent trigonometric ratio which is expressed as

Tan θ, = opposite side/adjacent side. Therefore,

Tan 70 = 35/h

h = 35/tan 70

h = 35/2.7475

h = 12.7 ft