Question

From the ends of a straight horizontal road 1km long, a balloon directly above the road is observed to have angles of elevation of 57◦and 33◦respectively. How to find the height of the balloon above the road ?

Answer 1

`0.457` km

Explanation:

Looking at the diagram. We are looking for the length of the perpendicular line AD.

Using triangle ACB

`/_CAB=180-(57+33)=90^@`

Using the sine rule:

`sinA/a=sinB/b=sinC/c`

Finding `bb(b)`

`sin(90^@)/1=sin(33)/b`

`1=sin(33)/b`

Rearranging:

`b=sin(33)=`AC

Looking at triangle ACD

`sin(57)=(AD)/(AC)=(AD)/b=(AD)/(sin(33)`

Rearranging:

`AD=sin(33)sin(57)=0.457`km 3 .d.p.