Question

Lance & Olga are standing on opposite sides of a lake. They both spot the same eagle flying above the lake at an altitude of 40 feet. Lance estimates the angle of elevation from the ground to the eagle to be 60° estimates the angle of elevation from the ground to the eagle to be 47°. How wide is the lake? Round your answer to the nearest tenth.

Answer 1

The width of the lake, estimated by Lance at a 60° angle of elevation, is approximately 23.1 feet. Olga's estimate, with a 47° angle of elevation, suggests a width of approximately 29.7 feet.

To find the width of the lake, we can use the tangent function in a right-angled triangle. Let d be the width of the lake.

For Lance's observation:

`\[ \tan(60^\circ) = (40)/(d) \]`

For Olga's observation:

`\[ \tan(47^\circ) = (40)/(d) \]`

Solving for \(d\) in both equations, we get:

`\[ d = (40)/(\tan(60^\circ)) \approx 23.1 \]\[ d = (40)/(\tan(47^\circ)) \approx 29.7 \]`

The width of the lake is approximately 23.1 feet according to Lance's estimate and 29.7 feet according to Olga's estimate.