Question

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.

Answer 1

Therefore, The climber's distance to the horizon = 171.20 miles

Explanation:

A climber is standing at the top of Mount Kilimanjaro, approximately 3.7 miles above sea level

⇒ Height of the climber from the sea level = 3.7 miles

The radius of the Earth is 3959 miles

⇒ Radius = 3959 miles.

Now, The line of sight L of the earth can be found by using the formula :

`L^2 + Radius^2=(Radius + Height)^2\\\\\implies L^2+3959^2=(3959+3.7)^2\\\\ \implies L^2 + 3959^2=3962.7^2\\\\\implies L^2=3962.7^2-3959^2\\\\\implies L^2 = 29310.29\\\\\implies L\approx 171.20\:\:miles`

Therefore, The climber's distance to the horizon = 171.20 miles

Answer 2

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