Can you help me with a trigonometry question?

Question

A plane moves from overhead to a position where the angle of elevation is 10 degrees, in 2 minutes. What is the speed of the plane given that it is constant and that the plane is travelling at a constant height of 4000m above the ground?

I don't know how to even get started, so please upload a diagram if possible and make the answer easy to understand.

Answer 1

This is a right triangle problem.

You need to be able to turn the words into pictures. Sometimes reading the words several times and working a little at a time helps.

Given that

The altitude (vertical leg) of the triangle is 4000m.

The right angle is at the overhead position from which the plane moves.

The base (horizontal leg) is the distance the plane moves.

The hypotenuse joins the horizontal and vertical legs.

The hypotenuse makes a 10° angle with the ground and an 80° angle with the altitude.

i.e. 90° - 10° = 80°

The hypotenuse makes a 10° angle with the horizontal leg.

Once you have the picture drawn, you exploit the tangent function to solve for the length of the horizontal leg.

Tan(80°) = h/4000

There fore

Tan(80°) = h/4000.