Question

Suppose you live 4.4 miles from the bottom of a hill. From your home, you see a plane directly above the hill. You estimate that the plane is about 2.5 miles in the sky from the bottom of the hill. You draw a diagram of the situation. Estimate the direct distance from you to the plane.

Answer 1

If you draw a diagram of the situation. You will see that the diagram will form a right triangle. Let us set the sides of the triangle as:
a = distance from you to the bottom of the hill = 4.4 miles
b = distance from the bottom of the hill to the plane = 2.5 miles
c = the direct distance of the plane from you = unknown

Since we have two given sides and we know that it is a right triangle, we use the Pythagorean theorem.
c^2 = a^2 + b^2
c^2 = 4.4^2 + 2.5^2
c = 5.06 miles

From the calculations, we see that the direct distance of the plane to you is 5.06 miles.