Question

a plane takes off at an angle of elevation of 15 degrees and travels in a straight line for 3,000 meters. What is the height of the plane above the ground at this instant?

Answer 1

SOH CAH TOA tells you the sine function of an angle gives the ratio of opposite side to the hypotenuse of the right triangle.
Sin = Opposite/Hypotenuse
In this problem, the angle is 15°, the hypotenuse is 3000 m and we want to find the length of the opposite side (the height above the ground).

sin(30°) = height/(3000 m)
Multiplying by 3000 m, we get
height = (3000 m)*sin(30°) = 1500 m

The height of the plane at that instant is ...
1500 m