In building a tent, Jada ties a rope from the top of a pole 3 meters high to a stake that is 4 meters away from the base of the pole. Jada draws this diagram to help find the angle made between the rope and the ground. pole rope 3
In building a tent, Jada ties a rope from the top of a pole 3 meters high to a stake that is 4 meters away from the base of the pole. Jada draws this diagram to help find the angle made between the rope and the ground. pole rope 3
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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Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
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Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
- The diagram illustrates a right triangle.
- The pole, indicated as vertical and measuring 3 meters, represents one side.
- The ground distance, marked as 4 meters, forms the horizontal side from the pole to the stake.
- The hypotenuse is the rope, which connects the top of the pole to the stake, and the angle \( x \) is formed between the rope and the ground.
The diagram can be summarized as follows:
- Vertical side (pole): 3 meters
- Horizontal side (ground): 4 meters
- Hypotenuse (rope): unknown
- Angle (\( x \)): between the hypotenuse and the horizontal side (ground)
### Which equation can Jada use to find the value of \( x \)?
Select the correct choice:
#### Options:
1. \( x = \tan\left(\frac{3}{4}\right) \)
2. \( \tan(x) = \frac{3}{4} \)
3. \( x = \tan\left(\frac{4}{3}\right) \)
4. \( \tan(x) = \frac{4}{3} \)
### Explanation:
To find the angle \( x \), you need to use the tangent function in trigonometry. Tangent (\( \tan \)) of an angle in a right triangle is defined as the opposite side divided by the adjacent side.
\[ \tan(x) = \frac{\text{opposite side}}{\text{adjacent side}} \]
In this case:
- The opposite side to angle \( x \) is 3 meters (the height of the pole).
- The adjacent side to angle \( x \) is 4 meters (the distance from the pole to the stake).
Thus:
\[ \tan(x) = \frac{3}{4} \]
Therefore, the correct equation is:
\[ \tan(x) = \frac{3}{4} \]
This corresponds to option 2 in the provided choices.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda1f6cc5-8a6c-4e05-8a10-05c0cc87bf21%2F66b948f1-af58-42aa-9bb9-52dc41bbd9fc%2Frljxs4n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining Angles in Right Triangles
In building a tent, Jada ties a rope from the top of a pole 3 meters high to a stake that is 4 meters away from the base of the pole.
Jada draws this diagram to help find the angle made between the rope and the ground.
- The diagram illustrates a right triangle.
- The pole, indicated as vertical and measuring 3 meters, represents one side.
- The ground distance, marked as 4 meters, forms the horizontal side from the pole to the stake.
- The hypotenuse is the rope, which connects the top of the pole to the stake, and the angle \( x \) is formed between the rope and the ground.
The diagram can be summarized as follows:
- Vertical side (pole): 3 meters
- Horizontal side (ground): 4 meters
- Hypotenuse (rope): unknown
- Angle (\( x \)): between the hypotenuse and the horizontal side (ground)
### Which equation can Jada use to find the value of \( x \)?
Select the correct choice:
#### Options:
1. \( x = \tan\left(\frac{3}{4}\right) \)
2. \( \tan(x) = \frac{3}{4} \)
3. \( x = \tan\left(\frac{4}{3}\right) \)
4. \( \tan(x) = \frac{4}{3} \)
### Explanation:
To find the angle \( x \), you need to use the tangent function in trigonometry. Tangent (\( \tan \)) of an angle in a right triangle is defined as the opposite side divided by the adjacent side.
\[ \tan(x) = \frac{\text{opposite side}}{\text{adjacent side}} \]
In this case:
- The opposite side to angle \( x \) is 3 meters (the height of the pole).
- The adjacent side to angle \( x \) is 4 meters (the distance from the pole to the stake).
Thus:
\[ \tan(x) = \frac{3}{4} \]
Therefore, the correct equation is:
\[ \tan(x) = \frac{3}{4} \]
This corresponds to option 2 in the provided choices.
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