A radio tower casts a shadow 170 feet long. The angle of elevation of the sun is 43 degrees. How high is the tower? Round to hundredths.
h/170 = tan43
evaluate tan43, multiply and you have h
180
To find the height of the tower, we can use the tangent function, since we know the angle of elevation and the shadow length.
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the height of the tower is the opposite side, and the shadow length is the adjacent side.
Let's denote the height of the tower as h.
Using the given angle of elevation and shadow length, we can set up the following equation:
tan(43 degrees) = h / 170 feet
To solve for h, we can rearrange the equation:
h = tan(43 degrees) * 170 feet
Using a calculator, we find that tan(43 degrees) is approximately 0.932477.
Plugging this value back into the equation, we can find the height of the tower:
h = 0.932477 * 170 feet
Calculating this value, we get:
h ≈ 158.52 feet
Therefore, the height of the tower is approximately 158.52 feet.