Question

2. A 13-foot ladder placed on level ground leans against the side of a house. The ladder reaches a point that is 12 feet up on the side of the house.

(a) What is the measure of the angle formed by the ladder and the level ground? Round your answer to the nearest degree. Show your work.
(b) The Occupational Safety and Health Administration (OSHA) sets standards for a variety of occupations to help prevent accidents and other safety hazards. OSHA’s standard for the angle formed by a ladder and level ground is . The same 13-foot long ladder is placed against the building according to OSHA’s safety standard.
What is the distance between the foot of the ladder and the foot of the building? Round your answer to the nearest tenth. Show your work.

Answer 1

a. x ≈ 67°(nearest degree)

b. distance = 5. 1 ft (nearest tenth)

Explanation:

A 13 ft ladder is placed on level ground leans against the side of a house . The ladder reaches a point that is 12 ft up the side of the house. The illustration forms a right angle triangle.

a. The right angle triangle formed has it opposite sides as 12 ft and it hypotenuse side as 13 ft. The angle formed between the ladder and the floor can be solved using sine ratio. Therefore,

let

x = angle

sin x = opposite/hypotenuse

sin x = 12/13

sin x = 0.92307692307

x = sin ⁻¹ 0.92307692307

x = 67.3801350509

x ≈ 67°(nearest degree)

b. If the same 13 ft ladder is placed against the building using the same angle formed .

The distance between the the foot of the ladder and the foot of the building is the adjacent side of the triangle. Therefore, using the angle formed.

cos 67° = adjacent/hypotenuse

cos 67° = adjacent/13

cross multiply

adjacent = 13 cos 67°

adjacent = 13 × 0.39073112848

adjacent = 5.07950467036

distance = 5. 1 ft(nearest tenth)

Answer 2

a) 67.4°

b) 5.0 ft

Explanation:

Now we have to use the trigonometric ratios to obtain the angle between the ladder and the level ground. Remember that the problem is a right angled triangle problem.

Let the hypotenuse of the triangle (length of the ladder) be c = 13 ft

Let the distance between the ladder and the ground be a

Let the height from the ground to the top of the ladder be b =12 ft

From;

Sinθ= opposite/hypotenuse

Sinθ= 12/13

Sinθ= 0.9231

θ=Sin^-1(0.9231)

θ= 67.4°

b) distance between the ladder and the foot of the building is obtained from

Cosθ= adjacent/hypotenuse

Adjacent= unknown

Hypotenuse= 13ft

θ= 67.4°

Cos(67.4°) = adjacent/13

Adjacent= cos (67.4°) ×13

Adjacent= 5.0 ft