5. A building 350 feet tall casts a 55-foot-long shadow. If you look down from the top of the building, what is the angle of depression of you to the end of the shadow? (Assume your eyes are level with the top of the building.)

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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**Problem: Calculating the Angle of Depression**

A building 350 feet tall casts a 55-foot-long shadow. If you look down from the top of the building, what is the angle of depression to the end of the shadow? (Assume your eyes are level with the top of the building.)

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**Solution Explanation:**

To solve for the angle of depression, we can use trigonometry. Imagine a right triangle where:

- The height of the building is the opposite side (350 feet).
- The length of the shadow is the adjacent side (55 feet).
- The angle of depression is the same as the angle of elevation from the end of the shadow to the top of the building.

Using the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle:

\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{350}{55}. \]

To find the angle \( \theta \), take the arctangent:

\[ \theta = \arctan\left(\frac{350}{55}\right). \]

Calculate \( \theta \) using a calculator to find the angle of depression.
Transcribed Image Text:**Problem: Calculating the Angle of Depression** A building 350 feet tall casts a 55-foot-long shadow. If you look down from the top of the building, what is the angle of depression to the end of the shadow? (Assume your eyes are level with the top of the building.) --- **Solution Explanation:** To solve for the angle of depression, we can use trigonometry. Imagine a right triangle where: - The height of the building is the opposite side (350 feet). - The length of the shadow is the adjacent side (55 feet). - The angle of depression is the same as the angle of elevation from the end of the shadow to the top of the building. Using the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{350}{55}. \] To find the angle \( \theta \), take the arctangent: \[ \theta = \arctan\left(\frac{350}{55}\right). \] Calculate \( \theta \) using a calculator to find the angle of depression.
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