Question

The angle of elevation of the sun (the angle the rays of sunlight make with the flat ground) at a particular time is 36°. At that time, how long is the shadow cast by a skyscraper that is 463 feet tall? Round to the nearest tenth of a foot.

Answer 1

To find the length of the shadow, use the tangent of the angle of elevation and the height of the skyscraper. The length of the shadow is approximately 649.1 feet.

Step-by-step explanation:

To find the length of the shadow cast by the skyscraper, we can use trigonometry. The angle of elevation of the sun is 36°, which means that the angle between the ground and the line from the top of the skyscraper to the sun is also 36°. Let's call the length of the shadow 'x'. We can set up the following equation:

tan(36°) = 463/x

Solving for x, we get:

x = 463/tan(36°)

Using a calculator, we find that x is approximately 649.1 feet. Rounding to the nearest tenth of a foot, the length of the shadow is 649.1 feet.