Answer:
Climber's distance to the horizon is 140.72 miles
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