Question

An airplane is approaching point A along a straight line and at a constant altitude h. At 10:00 am, the angle of elevation of the airplane is 20° and at 10:01 it is 60°. What is the altitude h of the airplane if the speed of the airplane is constant and equal to 600 miles/hour? (round answer to 2 decimal places).

Answer 1

consider the diagram below.

 

in this diagram, we use the known values with the relevant trigonometric ratios to find the unknown values. 

we start by determining the distance d(between B and C)

distance = speed X time

(1/60)*600 = 10 miles

we then express the tangent of the angles of elevation as shown below

tan 20 = h/(d+x)......................(i)

tan 60 = h/x .............................(ii)

we make h the subject of the formula in the two equations

h= tan 20(d+x)

h = tan 60(x)

we equate the expressions on the right-hand side in the two equations

tan20(10+x) = tan 60(x)

3.6397+0.36397x = 1.732x

we collect the like terms

3.6397=1.368x

dividing by 1.368 on both sides

x=2.66M.

from this, we can obtain the height 

h = 2.66tan 60

   =4.61M

the height is 4.61M