Question

Example 5

An air-traffic controller must quickly calculate the angle of descent (angle of depression)of
an incoming jet. He records from the jet's radio that its land distance is 44 km from the
control tower and the plane is flying at an altitude of 5.6 km. Find the angle of descent of
the plane (ignore the height of the control tower).

Answer 1

The angle of descent is 7.25°

Explanation:

Given:

Distance of landing from control tower = 44 km

Height of plane = 5.6 km

Consider a right angled triangle ABC such that AB = 5.6 km, BC = 44 km

So, angle of descent is given by 'x' as shown in figure below.

Now, from the figure, it is clear that,

Angle of descent = ∠ ACB ( Interior alternate angles are equal)

Now, from triangle ABC, the tangent of angle ACB is given as:

`\tan (\angle ACB)=(AB)/(BC)\\\\\tan(x)=(5.6)/(44)\\\\x=\tan^(-1)((5.6)/(44))\\\\x=7.25\°`

Therefore, the angle of descent is 7.25°.