Question

The Willis Tower in Chicago, United States. Dalila is 5.5 feet tall. She looks up at an angle of elevation of 50° to see the top, which is 1450 feet above the ground. Based on her measurements, calculate how far away she is from the base of the tower. Round to the nearest hundredth of a foot.

A. Approximately 882.96 feet
B. Approximately 2095.04 feet
C. Approximately 1551.66 feet
D. Approximately 880.32 feet

Answer 1

By using the tangent of the angle of elevation, we found that Dalila is approximately 1551.66 feet from the base of the Willis Tower, corresponding to answer choice C.

Step-by-step explanation:

To calculate the distance Dalila is from the base of the Willis Tower, we can use trigonometric ratios, specifically the tangent of the angle of elevation. Given that the angle of elevation is 50° and the height of the tower above her eye level is 1450 feet - 5.5 feet (her height), we use the tangent function to find the distance (d):

tangent(50°) = (1444.5 feet) / d

Solving for d:

d = 1444.5 / tangent(50°)

When you calculate this using a calculator set to degree mode, you will get:

d ≈ 1551.66 feet

Therefore, Dalila is approximately 1551.66 feet away from the base of the tower, which corresponds to answer choice C.