A painter is placing a ladder to reach the third story window, which is 39 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. The base of the ladder needs to be positioned 14.2 feet out from the building.

14.2 ft

Explanation:

The ladder form a right angle triangle with the horizontal angle of 70°

the angle faces the wall which is opposite to the ladder, the length of the ladder is the hypotenuse and the distance of the base from the wall is the adjacent

using trigonometrical ratio

tan 70° = opp (height of the wall) / adjacent, x (the distance of the base from the wall) = 39 ft / x

x = 39 ft / tan 70° = 14.195 approx 14.2 ft

41.5ft out from the building

Explanation:

The length of the ladder will serve as the hypotenuse of the right angled triangle formed by the set up. The height of the ladder above the ground is 39 feet to the top of the building where the ladder is placed.

Since the angle the ladder make to the base of the ladder is 70°, the opposite side of the set up will serve as the height.

According to SOH CAH TOA

Sin theta = Opposite/Hypotenuse

Sin 70° = 39ft/hypotenuse

Hypotenuse = 39/sin70°

Hypotenuse = 41.5feet

This means that the foot of the ladder must be placed 41.5feet out from the building.