Question

From the observation deck of the lighthouse at Sasquatch Point 55 feet above the surface of Lake Ippizuti, a lifeguard spots a boat out on the lake sailing directly toward the light

house. The first sighting had a angle of depression of 8.1 and the second sighting had an angle of depression of 25.7°. How far had the boat traveled between the sightings?

Answer 1

272.17 ft

Explanation:

Since the angle of depression of the sighting equals the angle of elevation of the lighthouse from the boat, using trigonometric ratios,

tanθ = x/d where θ = angle of sighting, x = height of lighthouse =55 ft and d = distance of boat from lighthouse at sighting

So, d = x/tanθ

when θ = 8.1°, for the first sighting,

d₁ = 55/tan8.1 = 386.45 ft

when θ = 25.7°, for the second sighting,

d₂ = 55/tan8.1 = 114.28 ft

The distance the boat traveled between the two sightings is thus d₁ - d₂ = 386.45 ft - 114.28 ft = 272.17 ft