Question

A 12 ft ladder leans against the side of a house. The bottom of the ladder is 5 ft away from the side of the house. Find x, the angle of elevation of the ladder.Round your answer to the nearest tenth of a degree.

Answer 1

x = 65.4°

Step-by-step explanation

In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.

So, after noting the three sides in a right triangle, we will then use trignometric ratios to solve for any of the unknown. If the non-right-angle angle given is x, the trignometric ratios in short forms are written as

SOH, CAH and TOA

SOH means Sin x = (Opp/Hyp)

CAH means Cos x = (Adj/Hyp)

TOA means Tan x = (Opp/Adj)

So, the one to be used depends on the sides of the triangle that are provided.

For this question,

Hypotenuse = 12

Opposite = ?

Adjacent = 5

Angle = x = ?

CAH means Cos x = (Adj/Hyp)

Cos x = (5/12)

Cos x = 0.4167

x = Cos⁻¹ (0.4167)

x = 65.4°

Hope this Helps!!!