Question

Find x, the angle of depression from the top of a lighthouse that is 153 ft above the water level to the waterline of a ship 1071 ft off shore. Round your answer to the nearest tenth of a degree.

Answer 1

The value of x to the nearest tenth of a degree is 8.1°

Using the concept of Trigonometry;

• Tan(θ) = opposite / Adjacent
• opposite = 153
• Adjacent = 1071

Inputting our values into the relation ;

Tan(θ) = (153 / 1071)

Tanθ = 153/1071

Tan(θ) = 0.142857

θ ≈ 8.1°

Answer 2

x = 8.1°

Explanation:

Reference angle = x

Opposite side = 153 ft

Adjacent side = 1071 ft

Applying trigonometric ratio (TOA), we have:

`tan(x) = (opp)/(adj)`

`tan(x) = (153)/(1071)`

`x = tan^(-1)((153)/(1071))`

`x = 8.1 degrees` (nearest tenth)