a 100 foot cliff drops vertically to a lake if the angle of elevation from a swimmer to the top of the cliff is 54.6 how far is the swimmer from the clif

Explanation:

Please see attached photo for explanation.

In the attached photo, X is the distance of the swimmer from the cliff.

Thus, we can obtain the value of x by using Tan ratio as illustrated below:

θ = 54.6°

Opposite = 100 foot

Adjacent = x =.?

Tan θ = Opposite /Adjacent

Tan 54.6 = 100/x

Cross multiply

x × Tan 54.6 = 100

Divide both side by Tan 54.6

x = 100 / Tan 54.6

x = 71.07 foot

Therefore, the swimmer is 71.07 foot from the cliff.