Question

Amelia is looking at the top of a lighthouse. She knows she is 30 feet from the base of

the lighthouse. If she is 5.5 feet tall and the angle of elevation is 34° how tall is the
lighthouse? Write only the number rounded to the nearest tenth of a foot.

Answer 1

25.7 feet

Explanation:

We are solving a right angled triangle.

We are the Trigonometric function of Tangent

tan θ = Opposite side/Adjacent

Angle of Elevation = θ = 34°

Opposite side = Height

Adjacent = 30 feet

tan 34° = Opposite side/30 feet.

Opposite side = tan 34° × 30 feet

Opposite side = 20.235255505 feet

The height of the light house =

Opposite side(height) + Amelia's height

20.235255505 feet + 5.5 feet

= 25.735255505 feet

Approximately to the nearest tenth ≈ 25.7 feet