Question

A hiker standing at point G wants to estimate the distance across the lake to point H, which is directly north of her location. She walks 700 feet west to point F. She measures the angle from point F to point H to be 78º north of east. Find the distance across the lake to the nearest tenth of a foot.

Answer 1

c. 3,293.2 feet

Explanation:

Answer 2

Refer to the figure shown below.

Let x = distance across the lake (from G to H).

FG = distance walked west of G.
m∠GFH = 78°, north of east.

By definition, tan 78° = x/70
Therefore,
x = 70*(tan 78°) = 329.3 ft (nearest tenth)

Answer: 329.3 ft