Question

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

Answer 1

We know Hypotenuse, and we are trying to find Adjacent. Hence, we need to use cosine.

Let X be the distance between the buildings.

cos17° = X/10

X = 10cos17° = 9.56 yards

Answer 2

9.56 yards apart.

Explanation:

Let x represent distance between both buildings.

We have been given that a clothes-line is connected from a window on one building to a window in a building across the alley. The clothes line is 10 yards long with an angle of depression of 17 degrees.

First of all, we will draw a graph to represent our given scenario.

We know that cosine relates adjacent side of right triangle to hypotenuse.

`\text{cos}=\frac{\text{Adjacent}}{\text{hypotenuse}}`

`\text{cos}(17^(\circ))=(x)/(10)`

`x=10\cdot \text{cos}(17^(\circ))`

`x=10\cdot 0.956304755963`

`x=9.56304755963`

`x\approx 9.56`

Therefore, the both buildings are 9.56 yards apart.