Question

From the top of a 150 m high-rise building,

two cars on the same road below the

building are seen at an angle of depression

of 45° and 60° on each side of the tower.

Find the distance between the two cars,

correct to the nearest metre.

Answer 1

The distance between the two cars is approximately 237 meters.

Explanation:

Let be P the top of the high-rise building and Q and R the location of the two cars from each side of the tower. Geometric figure is represented on image attached below. We calculate the distance between both cars (
`d`), measured in meters, by Trigonometric ratios:

`d = QO + OR`

`d = (OP)/(\tan 45^(\circ)) +(OP)/(\tan 60^(\circ))`

Where
`OP` is the height of the building, measured in meters.

`d = OP\cdot \left((1)/(\tan 45^(\circ) )+(1)/(\tan 60^(\circ)) \right)`

If we know that
`OP = 150\,m`, then:

`d = (150\,m)\cdot \left((1)/(\tan 45^(\circ))+(1)/(\tan 60^(\circ)) \right)`

`d \approx 236.603\,m`

The distance between the two cars is approximately 237 meters.