Question

A guy wire makes a 65° angle with the ground. walking out 37 feet further from the tower, the angle of elevation to the top of the tower is 39°. find the height of the tower, rounded to the nearest whole foot.

Answer 1

48ft

Explanation:

I got it correct on founders edtell

Answer 2

Let's call the height of the tower
`h` and the distance from the 65 degree angle to the base of the tower
`d`.

We get two equations:

`\tan 65^\circ = \frac h d`

`\tan 39^\circ = (h)/(d+37)`

`h = d \tan 65^\circ = (d+37) \tan 39^\circ`

`d(\tan 65 - \tan 39) = 37 \tan 39`

`d = (37 \tan 39)/(\tan 65 - \tan 39)`

`h = d \tan 65 = (37 \tan 39 \tan 65)/(\tan 65 - \tan 39)`

`h \approx 48.1 \textrm{ feet}`

Answer: 48