A climber is standing at the top of Mount Kilimanjaro, approximately 3.7 mi above sea level. The radius of the Earth is 3959 mi. What is the climber's distance to the horizon? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

Question

Mathematics

Zimmerman

1 July, 21:58

A climber is standing at the top of Mount Kilimanjaro, approximately 3.7 mi above sea level. The radius of the Earth is 3959 mi. What is the climber's distance to the horizon? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

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Answers (1)

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Kinsley · Answer 1

We are given

height = 3.7 mi

radius = 3959 mi

We are asked for the distance between the man and the horizon

The straight line from the man to the horizon is a tangent line to the surface of the earth

Using Pythagorean theorem

(3.7 + 3959) ² = 3959² + d²

Solve for d

d = 171 mi