Question

Susan and Mark are standing at different places on a beach and watching a bird. The angles of elevation they make are 20º and 50º, respectively. If Susan and Mark are 7 kilometers apart and the bird is between them, the bird is at a height of kilometers from the ground. NextReset

Answer 1

The answer is 1.952 km

Answer 2

The bird is at a height of 1.95 km from the ground.

Explanation:

It is given that the distance between susan and mark is 7 km and bird is between susan and mark. The angles of elevation they make are 20º and 50º, respectively.

Draw a perpendicular line from the bird on base.

Let the distance of susan from and the altitude be x.

In triangle ABS,

`tan(20^(\circ))=(AB)/(x)`

`tan(20^(\circ))x=AB`

`0.364x=AB` ..... (1)

In triangle ABM,

`tan(50^(\circ))=(AB)/(7-x)`

`1.192(7-x)=AB` ..... (2)

From (1) and (2), we get

`0.364x=1.192(7-x)`

`1.556x=8342`

`x=5.36`

The length of AB is,

`AB=0.364(5.36)=1.95147\approx 1.95`

Therefore, the he bird is at a height of 1.95 km from the ground.