Question

Photo attached***. Chris works in the tall building across the street from Tam. From the top of this building Chris observes the angle of depression of the top of Tam’s building to be 10°. The angle of depression of the bottom of Tam’s building is 25°.

(a) Find the width of the street.
b) Find the height of Tam’s building

Answer 1

Width of the street = 128.67 m

Height of Tam’s building = 37.31 m

Explanation:

25° is the angle of depression from the top of Chris's building to the bottom of Tam's building

If the height of Chris's building is 60 m and the width if the road is x m,

then we can write

`\tan 25 = (60)/(x)`

⇒
`x = (60)/(\tan 25) = 128.67` m. (Answer)

Now, if the height of Chris's building is y m more than Tam's building and the angle of depression of top of Tam's building from top of Chris's building is 10°, then we can write,

`\tan 10 = (y)/(128.67)`

⇒ y = 22.69 m

Therefore, Tam's building height is (60 - 22.89) = 37.31 m (Answer)