Question

Mary is standing out on the balcony of her apartment which is 40 feet above the ground and looks up at a 31° angle to see her friend Sue who is standing on her balcony. If Mary and Sue's apartments are 20 feet apart from one another, how high off the ground is Sue?

Answer 1

52 feet

Explanation:

This situation can be represented by the attached figure as in the answer area.

Let M be the location of Mary.

Let S be the location of Sue.

Distance between apartments is given as 20 feet.

Distance between ground and balcony of Mary is 40 feet.

There is a right angled
`\triangle MOS`.

`\angle OMS = 31^\circ`

To find:

The distance SO + 40 feet.

We can use tangent ratio here in right angled
`\triangle MOS`.

`tan\theta = (Perpendicular)/(Base)`

`tan31^\circ = (SO)/(MO)\\\Rightarrow tan31^\circ = (SO)/(20)\\\Rightarrow SO=20* 0.6\\\Rightarrow \bold{SO=12\ ft}`

Height of Sue above ground = 40+12 = 52 feet