Aclimber is standing at the top of a mountain, approximately 2.5 miles above sea level. the radius of the earth is 3959 miles. 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.

Climber's distance to the horizon is 140.72 miles

Step-by-step explanation:

In the figure attached, climber is at point A at the top of a mountain.

O is the center of the earth and distance from the center of the earth to the climber is (r + 2.5) miles.

Point B is the horizon.

We have to calculate the distance AB which is the climber's distance to the horizon.

Now we know radius OB will be perpendicular to the distance AB, tangent drawn to the circle O.

Now we apply Pythagoras theorem in ΔOAB

AO² = AB² + OB²

(r + 2.5)² = AB² + r²

Since radius of earth r = 3959 miles

By substituting the value of r,

(3959 + 2.5)² = AB² + 3959²

(3961.5)² = AB² + 3959²

15693482.25 = AB² + 15673681

AB² = 15693482.25 - 15673681

      = 19801.25

AB = 140.72 miles

Therefore, climber's distance to the horizon will be 140.72 miles

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