Ques29 **Problem 29: Determining the Height of a Telephone Pole Using Trigonometry**In this problem, we are given a telephone pole that casts a 23-foot shadow along the ground. The angle of elevation of the Sun is specified to be 69°. We need to determine which equation can be used to calculate the height $ h $ of the telephone pole.**Diagram Description:**The provided diagram depicts a right triangle. The triangle consists of the following elements:- The vertical leg represents the height ($ h $) of the telephone pole.- The horizontal leg represents the shadow cast by the pole, which measures 23 feet.- The hypotenuse is the slanting line drawn from the top of the pole to the end of the shadow on the ground.- An angle of 69° is shown between the horizontal leg and the hypotenuse, indicating the angle of elevation of the Sun.The task is to identify the correct trigonometric equation that relates these dimensions.**Answer Choices:**- **A.** $ \tan 69^\circ = \frac{23}{h} $- **B.** $ \cos 69^\circ = \frac{23}{h} $ (This answer is selected)- **C.** $ \tan 69^\circ = \frac{h}{23} $- **D.** $ \cos 69^\circ = \frac{h}{23} $In a right triangle:1. **Tangent ($ \tan $)** of an angle is the ratio of the opposite side to the adjacent side.2. **Cosine ($ \cos $)** of an angle is the ratio of the adjacent side to the hypotenuse.Given the information:- The opposite side to the 69° angle is $ h $ (height of the pole).- The adjacent side to the 69° angle is 23 feet (length of the shadow).Considering the right triangle computations:- The tangent relationship would ideally be $ \tan 69^\circ = \frac{h}{23} $, which matches option C.- The cosine relationship involving the shadow and the hypotenuse is incorrect in the context of solving for $ h $.Thus, in this context, the correct option is **C**: $ \tan 69^\circ = \frac{h}{23} $.The checkbox

Name: Ques29 **Problem 29: Determining the Height of a Telephone Pole Using
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Description: Ques29 **Problem 29: Determining the Height of a Telephone Pole Using Trigonometry**In this problem, we are given a telephone pole that casts a 23-foot shadow along the ground. The angle of elevation of the Sun is specified to be 69°. We need to dete

Answered: 29. A telephone pole casts a 23-foot…

Math

Geometry

29. A telephone pole casts a 23-foot shadow along the ground when the angle of elevation of the Sun is 69'.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Ques29

**Problem 29: Determining the Height of a Telephone Pole Using Trigonometry**

In this problem, we are given a telephone pole that casts a 23-foot shadow along the ground. The angle of elevation of the Sun is specified to be 69°. We need to determine which equation can be used to calculate the height $ h $ of the telephone pole.

**Diagram Description:**
The provided diagram depicts a right triangle. The triangle consists of the following elements:
- The vertical leg represents the height ($ h $) of the telephone pole.
- The horizontal leg represents the shadow cast by the pole, which measures 23 feet.
- The hypotenuse is the slanting line drawn from the top of the pole to the end of the shadow on the ground.
- An angle of 69° is shown between the horizontal leg and the hypotenuse, indicating the angle of elevation of the Sun.

The task is to identify the correct trigonometric equation that relates these dimensions.

**Answer Choices:**
- **A.** $ \tan 69^\circ = \frac{23}{h} $
- **B.** $ \cos 69^\circ = \frac{23}{h} $ (This answer is selected)
- **C.** $ \tan 69^\circ = \frac{h}{23} $
- **D.** $ \cos 69^\circ = \frac{h}{23} $

In a right triangle:
1. **Tangent ($ \tan $)** of an angle is the ratio of the opposite side to the adjacent side.
2. **Cosine ($ \cos $)** of an angle is the ratio of the adjacent side to the hypotenuse.

Given the information:
- The opposite side to the 69° angle is $ h $ (height of the pole).
- The adjacent side to the 69° angle is 23 feet (length of the shadow).

Considering the right triangle computations:
- The tangent relationship would ideally be $ \tan 69^\circ = \frac{h}{23} $, which matches option C.
- The cosine relationship involving the shadow and the hypotenuse is incorrect in the context of solving for $ h $.

Thus, in this context, the correct option is **C**: $ \tan 69^\circ = \frac{h}{23} $.

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