Angles of elevation and Trigonometry

Question

Mount Mayon is an active volcano on the island of Luzon in the Philippines. At an unknown distance from the volcano, the angle of elevation to the peak of the volcano is approximately 26.22◦. Exactly 1000 metres closer to the volcano, the angle of
elevation to the volcano’s peak increases to approximately 31.62◦. Use the given information to estimate the height of Mount Mayon.

Answer 1

Draw and label a diagram.

The base of the mountain is C

Your first position is A

Your second position is B

h represents the height of the mountain.

tan 26.22 = h / (CB + 1000)

(CB + 1000) tan 26.22 = h

tan 31.62 = h / CB

CB tan 31.62 = h

(CB + 1000) tan 26.22 = CB tan 31.62

 

Can you solve for h and answer?