Question

The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:____________A. 2.3 mB. 4.6 mC. 7.8 mD. 9.2 m

Answer 1

Answer: 9.2m

Explanation: According to SOH CAH TOA

Cos 60° = Adjacent/Hypotenuse (CAH)

Given theta = 60° which is the elevation angle

Adjacent side which is the base of the set up (distance from the ladder to the wall) is 4.6m

Cos60° = Adjacent/Hypotenuse

Cos 60° = 4.6/Hypotenuse

Hypotenuse = 4.6/cos60°

Hypotenuse = 9.2m

The hypotenuse always the slanting and longest side of the set up which is the ladder according to the question.

Answer 2

Answer: D. 9.2 m

The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:____________A. 2.3 mB. 4.6 mC. 7.8 mD. 9.2 m

Explanation:

Given;

Angle of elevation A= 60°

Distance from the foot of the ladder to the wall x= 4.6m

Length of the ladder = L

CosA = adjacent/hypothenus = x/L

L = x/cosA

L = 4.6/cos60°

L = 9.2m

The length of the ladder is 9.2m