A tower casts a 235-foot-long shadow. If the angle of elevation from the tip of the shadow to the top of the tower is 66.3°, how high is the tower?
To find the height of the tower, we can use trigonometry. Specifically, we can use the tangent function, which relates the angle of elevation to the height and the length of the shadow.
The tangent function can be expressed as follows:
tan(angle of elevation) = height of the tower / length of the shadow
We are given that the angle of elevation is 66.3° and the length of the shadow is 235 feet. Plugging these values into the equation, we get:
tan(66.3°) = height of the tower / 235
To find the height of the tower, we need to isolate the height on one side of the equation. We can accomplish this by multiplying both sides of the equation by 235:
235 * tan(66.3°) = height of the tower
Now we can use a calculator to evaluate the right side of the equation:
235 * tan(66.3°) ≈ 603.118
So the height of the tower is approximately 603.118 feet.