---**Problem: Determining the Height of a Tree**Tim wants to determine the height, $ x $, of a nearby tree. He stands 35 feet from the base of the tree. The measure of the angle of elevation from Tim to the top of the tree is 40 degrees. **Select one of the following** that can be used to find the height of the tree.- $\boxed{\ } x = \frac{35}{\tan 40}$- $\boxed{\ } x = 35 \cos 40$- $\boxed{\ } x = 35 \sin 40$- $\boxed{\ } x = 35 \tan 40$- $\boxed{\ } x = \frac{35}{\sin 30}$**Explanation:**To solve this problem, you should use trigonometric functions and understand basic right triangle relationships. In this context, we use the tangent function, which relates the angle of elevation to the opposite side (the height of the tree) and the adjacent side (the distance from Tim to the base of the tree).The correct formula to use is:\[ x = 35 \tan 40 \]This is because tangent is defined as:\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]In this problem, the opposite side is $ x $ (the height of the tree), and the adjacent side is 35 feet. Hence:\[ \tan(40^\circ) = \frac{x}{35} \]Rearranging gives:\[ x = 35 \tan 40^\circ \]By understanding this relationship, you can correctly choose the equation that allows you to find the height of the tree.

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Description: ---**Problem: Determining the Height of a Tree**Tim wants to determine the height, $ x $, of a nearby tree. He stands 35 feet from the base of the tree. The measure of the angle of elevation from Tim to the top of the tree is 40 degrees. **Select

The top of the tree, Tim and the base of the tree form a right triangle. The tree measures feet…

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Tim wants to determine the height, x, of a nearby tree. He stands 35 feet from the base of the tree. The measure of the angle of elevation from Tim to the top of the tree is 40 degrees. Select one of the following that can be used to find the height of the tree. tan 40 35 cos 40 I = 35 sin 40 35 tan 40 35 sin 50

Tim wants to determine the height, x, of a nearby tree. He stands 35 feet from the base of the tree. The measure of the angle of elevation from Tim to the top of the tree is 40 degrees. Select one of the following that can be used to find the height of the tree. tan 40 35 cos 40 I = 35 sin 40 35 tan 40 35 sin 50

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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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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**Problem: Determining the Height of a Tree**

Tim wants to determine the height, $ x $, of a nearby tree. He stands 35 feet from the base of the tree. The measure of the angle of elevation from Tim to the top of the tree is 40 degrees. **Select one of the following** that can be used to find the height of the tree.

- $\boxed{\ } x = \frac{35}{\tan 40}$
- $\boxed{\ } x = 35 \cos 40$
- $\boxed{\ } x = 35 \sin 40$
- $\boxed{\ } x = 35 \tan 40$
- $\boxed{\ } x = \frac{35}{\sin 30}$

**Explanation:**

To solve this problem, you should use trigonometric functions and understand basic right triangle relationships. In this context, we use the tangent function, which relates the angle of elevation to the opposite side (the height of the tree) and the adjacent side (the distance from Tim to the base of the tree).

The correct formula to use is:
\[ x = 35 \tan 40 \]

This is because tangent is defined as:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this problem, the opposite side is $ x $ (the height of the tree), and the adjacent side is 35 feet. Hence:
\[ \tan(40^\circ) = \frac{x}{35} \]
Rearranging gives:
\[ x = 35 \tan 40^\circ \]

By understanding this relationship, you can correctly choose the equation that allows you to find the height of the tree.

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