Question

A radio tower has a 46-foot shadow cast by the sun. If the angle from the tip of the shadow to the top of the tower is 82 degrees , what is the height of the radio tower? Roundyour solution to four decimal places.

Answer 1

The height of the radio tower is 327.3070 feet.

EXPLANATION

Let's first sketch the problem.

From the sketch above, adjacent = 46 θ=82

opposite = h (height of the radio tower.

Using the trigonometric ratio,

$\tan \theta=\frac{\text{opposite}}{\text{adjacent}}$

$\tan 82=\frac{h}{46}$

Cross-multiply

$h=46\times\tan 82$

h ≈ 327.3070 feet.

Therefore, the height of the radio tower is 327.3070 feet.