Isaac is looking through binoculars on a whale watching trip when he notices a sea otter in the distance. If he is 20 feet above sea level in the boat, and the angle of depression is 30 degrees, how far away from the boat is the otter (to the nearest foot) ?

Question

Keith Roy

Mathematics

12 October, 10:42

Isaac is looking through binoculars on a whale watching trip when he notices a sea otter in the distance. If he is 20 feet above sea level in the boat, and the angle of depression is 30 degrees, how far away from the boat is the otter (to the nearest foot) ?

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Answers (1)

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Porter Small · Answer 1

Tan of an angle = perpendicular / base

Here, perpendicular is the side of the triangle opposite the angle.

And base is the arm of the angle other the hypotenuse.

If the side of the triangle to be found (marked as? in the figure) is x, then

perpendicular = 20 feet

base = x

so, tan 30 = 20/x

so, x = 20 / (tan 30 degrees) = 34.64 feet

= 35 feet to the nearest foot