Amountain climber is at an altitude of 2.9 mi above the earth’s surface.

from the climber’s viewpoint, what is the distance to the horizon?

Using Pythagoras theorem:

.

We know that:

The radius of a circle meets a tangent at 90 degree

Labelled the triangle as A, B and C as shown below;

In rt angle triangle ABC:

Opposite side = AB = x units

Adjacent side = BC = 3959 mi

Hypotenuse side=AC = 3959 +2.9 = 3961.9 mi

Using Pythagoras theorem;

then;

⇒

⇒

Simplify:

151.560549 = x

or

x = 151.6 mi

Therefore, the distance to the horizon From the climber’s viewpoint is, 151.6 mi