Question

A clothes line is connected from a window on one building to a window in a building across the alley. The clothesline is 10 yards long with an angle of depression of 17°. How far apart are the buildings?

Answer 1

The distance between the two buildings is 9.563 yards.

Explanation:

See the diagram attached.

AB and CD are two buildings AC distance apart.

Now, AC = ED.

The angle of depression of clothesline BD is 17 Degrees.

Now, given that BD = 10 yards.

And ∠ OBD = ∠ BDE = 17° {Alternate angles}

Now, from the right triangle Δ BED, we have

`\cos 17 = (ED)/(BD) = (ED)/(10)`

⇒ ED = 10 cos 17 = 9.563 yards.

Therefore, the distance between the two buildings is 9.563 yards. (Answer)