Question

William spots a tree directly across the river from where he is standing. He then walks 20 ft upstream and determines that the angle between his previous position and the tree on the other side of the river is 65°. How wide is the river?

Answer 1

In my opinion, the width of the river is 16.537ft.

Answer 2

This shows that the river is 8.45 feet wide

The set up forms a right triangle. The width of the river is adjacent of the triangle (h).

The distance walked by William will be the hypotenuse (l)

Using the SOH CAH TOA identity:

Cos theta = adjacent/hypotenuse

Cos 65 = h/l

Cos 65 = h/20

h = 20 cos 65

h = 20 (0.4226)

h = 8.45 feet

This shows that the river is 8.45 feet wide

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