Question

A radio tower has a 28-foot shadow cast by the sun. If the angle from the tip of the shadow to the top of the tower is 69, what is the height of theradio tower? Round your solution to four decimal places.

Answer 1

We can see here that the height of the radio tower is approximately 72.9425 ft.

To find the height of the radio tower, we can use trigonometry, specifically the tangent function. The tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

In this case, the tangent of the angle formed by the shadow and the height of the tower can be used to find the height of the tower.

Let ℎ be the height of the tower, and the length of the shadow be 28 feet.

The tangent of the angle 69 degrees can be written as:

tan(69°) = height of tower/height of shadow

tan(69°) = h/28

Now, solve for the height, ℎ:

h = 28 × tan (69°)

h = 28 × 2.6051 = 72.9425 ft.

The height of the radio tower is approximately 72.9425 ft.

Answer 2

72.9425 feet

Step-by-step explanation:

Let's sketch an image of the question;

To determine the height of the radio tower(h), we have to take the tangent of angle 69 degrees;

`\begin{gathered} \tan 69=(h)/(28) \\ h=28\tan 69 \\ h=72.9425ft \end{gathered}`

Therefore, the height of the radio tower is 72.9425 feet.