Question

From the top of a vertical tower, 331 feet above the surface of the earth, the angle of depression to a doghouse is 28 degrees 8'. How far is it from the doghouse to the foot of the tower?

Answer 1

Answer:

619.13 feet

Step-by-step explanation:

Please find the attachment.

Let x represent the distance between doghouse to the foot of the tower.

We have been given that from the top of a vertical tower, 331 feet above the surface of the earth, the angle of depression to a doghouse is 28 degrees 8'. We are asked to find the distance between doghouse to the foot of the tower.

First of all, we will convert our given angle into degrees as it is given in degrees and minutes.

We will divide 8 by 60 to convert 8 minutes into degrees as:

$\frac{8}{60}=0.13333$

The doghouse, tower and angle of depression forms a right triangle with respect to ground, where, 331 feet is opposite side and x is adjacent side to angle 28.13 degrees.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(28.13^{\circ})=\frac{331}{x}$

$x=\frac{331}{\text{tan}(28.13^{\circ})}$

$x=\frac{331}{0.534623339864}$

$x=619.12747783$

Upon rounding to nearest hundredth, we will get:

$x\approx 619.13$

Therefore, the doghouse is 619.13 feet far from the foot of the tower.