Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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A 20 meter tall statue casts a shadow that is 10 meters long. Will sketches the following diagram to help find the
![**Title: Finding the Angle of Elevation Using Trigonometry**
**Introduction**
This tutorial will help you understand how to find the angle of elevation from the ground to the sun using trigonometric principles. We will use a real-world example where a 20 meter tall statue casts a 10 meter long shadow.
**Problem Statement**
A 20 meter tall statue casts a shadow that is 10 meters long. Will sketches the following diagram to help find the angle of elevation from the ground to the sun. Which equation can Will use to find the value of \(x\)?
**Diagram Explanation**
There is a right triangle in the diagram with:
- The height of the statue (opposite side) labeled as 20 meters.
- The length of the shadow (adjacent side) labeled as 10 meters.
- The right angle (90 degrees) is between the height of the statue and the shadow.
- The angle of elevation \(x\) is located between the ground and the hypotenuse.
**Mathematical Approach**
To solve for the angle of elevation \(x\), we use the tangent trigonometric function. The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.
This can be mathematically represented as:
\[
\tan(x) = \frac{\text{opposite}}{\text{adjacent}}
\]
Substituting the given values:
\[
\tan(x) = \frac{20}{10}
\]
\[
\tan(x) = 2
\]
**Question Options**
Given these concepts, the problem provides multiple-choice options to determine the correct trigonometric equation to find \(x\):
- \( \tan(x) = \frac{10}{20} \)
- \( \tan(x) = \frac{20}{10} \)
- \( x = \tan \left( \frac{20}{10} \right) \)
- \( x = \tan \left( \frac{10}{20} \right) \)
**Answer**
The correct option is:
\[
\tan(x) = \frac{20}{10}
\]
**Conclusion**
By understanding and applying the tangent function and the relation between the sides of a right triangle, we can easily determine that the angle of elevation \(x\) can be found using the equation \(\tan(x) = \frac{20}{](https://content.bartleby.com/qna-images/question/ce362edb-c002-49f1-add1-d9933973e98b/7067eef4-4631-42bd-b50b-c0ffa9ed6c9d/ztf6qy6_processed.jpeg)
Transcribed Image Text:**Title: Finding the Angle of Elevation Using Trigonometry**
**Introduction**
This tutorial will help you understand how to find the angle of elevation from the ground to the sun using trigonometric principles. We will use a real-world example where a 20 meter tall statue casts a 10 meter long shadow.
**Problem Statement**
A 20 meter tall statue casts a shadow that is 10 meters long. Will sketches the following diagram to help find the angle of elevation from the ground to the sun. Which equation can Will use to find the value of \(x\)?
**Diagram Explanation**
There is a right triangle in the diagram with:
- The height of the statue (opposite side) labeled as 20 meters.
- The length of the shadow (adjacent side) labeled as 10 meters.
- The right angle (90 degrees) is between the height of the statue and the shadow.
- The angle of elevation \(x\) is located between the ground and the hypotenuse.
**Mathematical Approach**
To solve for the angle of elevation \(x\), we use the tangent trigonometric function. The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.
This can be mathematically represented as:
\[
\tan(x) = \frac{\text{opposite}}{\text{adjacent}}
\]
Substituting the given values:
\[
\tan(x) = \frac{20}{10}
\]
\[
\tan(x) = 2
\]
**Question Options**
Given these concepts, the problem provides multiple-choice options to determine the correct trigonometric equation to find \(x\):
- \( \tan(x) = \frac{10}{20} \)
- \( \tan(x) = \frac{20}{10} \)
- \( x = \tan \left( \frac{20}{10} \right) \)
- \( x = \tan \left( \frac{10}{20} \right) \)
**Answer**
The correct option is:
\[
\tan(x) = \frac{20}{10}
\]
**Conclusion**
By understanding and applying the tangent function and the relation between the sides of a right triangle, we can easily determine that the angle of elevation \(x\) can be found using the equation \(\tan(x) = \frac{20}{
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