Question

How far from the base of a building must the bottom of a 15-foot ladder sit in order for it to make a 52 angle with the ground? round to the nearest tenth of a foot.

Answer 1

Answer:

9.2 ft

Step-by-step explanation:

The length of the ladder is 15 ft

The ladder makes an angle of 52° with the ground

The distance (x) from the base of the house to the foot of the ladder is given by;

$\frac{x}{15}$ = cos 52°

x = 15 × cos 52° = 9.23492213 ft

Which equals to 9.2 ft (rounded off to tenth of a foot)

Answer 2

The distance between the base of the building and the bottom of the ladder is 11.72 feet.

It is given that

Length of the ladder = 15 feet

The angle of inclination = 52°

Let us say the distance between the base of the building and the bottom of the ladder is x.

What is the tangent of an angle?

The tangent of an angle is the ratio of the opposite side(to that angle) to the base of the triangle.

Tan 52° = length of the ladder / distance between base of building and bottom of the ladder.

Tan 52 = 15/x

x= 15/Tan 52

x = 11.72 feet.

Therefore, The distance between the base of the building and the bottom of the ladder is 11.72 feet.

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