Question

To input your angle measures in degrees, use the functions sind, cosd and tand, instead of sin, cos and tan. Zach stands at the top of a cliff. On the ground, 310 feet below, Zach spots a coyote. When Zach initially sees the coyote, the angle of depression for his vision is 6 degrees. Draw a picture! At this point in time, how far is the coyote from the base of the cliff

Answer 1

about 2949 feet

Explanation:

The geometry of the situation can be modeled by a right triangle. The height of the cliff can be taken to be the side opposite the given angle, and the distance to the coyote will be the side adjacent to the given angle. The relation between these values is the trig function ...

Tan = Opposite/Adjacent

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setup

Filling in the known values, we have ...

tan(6°) = (310 ft)/(distance to coyote)

solution

Multiplying by (distance to coyote)/tan(6°) gives ...

distance to coyote = (310 ft)/tan(6°) ≈ 310/0.105104 ft

distance to coyote ≈ 2949.453 ft

The coyote is about 2949 feet from the base of the cliff.