Apple And Pie Question

Question

Apple and Pie stand near the foot of a tall mountain and measure their angles of elevation to the summit of the mountain T. Apple stands at point A and measures 37°. Pie stands at point P and measures 45°. They also measure the distance between them to be 7km. If A, T, and P are on the same straight line, estimate the height of the mountain to the nearest integer in metres (m).

Answer 1

tan 37 = h/x

tan 45 = h(7-x)

x*tan 37 = h and (7-x) tan 45 =h

x tan 37 = (7-x) tan 45

x tan 37 = 7 * tan 45 - x * tan 45

x tan 37 + x * tan 45 = 7 tan 45

x ( tan 37 + tan 45) = 7 tan 45

x = 7 * tan 45 / (tan 37 + tan 45)

x = 3.9918929214583700639334119270148+ <--- it is almost 4

tan 37 = h/x ---> h = x * tan 37 = 3.0081070785416299360665880729851+ km