Question

A guy wire makes a 67° angle with the ground. Walking out 32 feet further from the tower, the angle of elevation to the top of the tower is 39°. Find the height of the tower.A. 40 ftB. 86 ftC. 48 ftD. 58 ft

Answer 1

The height of the tower will be given by:

`\tan\theta=(opposite)/(adjacent)`

Where:

opposite = h

adjacent = x

tetha = 67°

Therefore:

`\tan67=(h)/(x)`

Solve for h:

`\begin{gathered} x\cdot\tan67=x\cdot(h)/(x) \\ h=x\cdot\tan67 \end{gathered}`

And for the other angle:

`\tan39=(h)/(x+32)`

Solve for h:

`h=(x+32)\cdot\tan39`

Equating the two equations for h, we have:

`x\tan67=(x+32)\tan39`

Now, solve for x:

`\begin{gathered} x(2.36)=(x+32)(0.81) \\ 2.36x=0.810x+25.92 \\ 2.36x-0.81x=0.81x+25.92-0.81x \\ 1.55x=25.92 \\ (1.55x)/(1.55)=(25.92)/(1.55) \\ x=16.72\approx17 \end{gathered}`

Now, we find h:

`h=17\cdot\tan67=40.05\approx40`

Answer: A 40 ft