Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section3.1: Law Of Sines
Problem 4ECP: Show that there is no triangle for which a=4 feet, b=14 feet, and A=60.
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![In the provided image, we have a right triangle. Here's a detailed explanation and transcription of the elements of the diagram:
### Diagram Explanation:
- The triangle is a right triangle, indicated by a small square at the angle.
- The length of the horizontal leg (base) of the triangle is labeled as 38.
- The length of the vertical leg (height) of the triangle is labeled as 27.
- The hypotenuse (the side opposite the right angle) is not labeled with a length, but the angle adjacent to the base and the hypotenuse is marked with a question mark (?), indicating that this is the angle we need to find.
### Steps to Find the Missing Angle:
1. **Identify the Known Elements:**
- Base (adjacent side) = 38
- Height (opposite side) = 27
2. **Use Trigonometric Ratios:**
- Since we need to find the angle, we can use the tangent function, which is the ratio of the opposite side to the adjacent side.
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
\[
\tan(\theta) = \frac{27}{38}
\]
3. **Calculate the Angle:**
- Use the arctangent function (tan^(-1)) to find the angle.
\[
\theta = \tan^{-1}\left(\frac{27}{38}\right)
\]
- Calculate this value using a calculator or trigonometric tables.
By performing the calculation, students will find the value of the angle marked with the question mark. This method demonstrates practical usage of trigonometric functions in solving right triangle problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f3e5dad-3eef-4af4-8432-92621aeb9e2a%2Fd592a668-2d97-4cf8-ada4-88e3fcbfe3a9%2F1ajqebc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In the provided image, we have a right triangle. Here's a detailed explanation and transcription of the elements of the diagram:
### Diagram Explanation:
- The triangle is a right triangle, indicated by a small square at the angle.
- The length of the horizontal leg (base) of the triangle is labeled as 38.
- The length of the vertical leg (height) of the triangle is labeled as 27.
- The hypotenuse (the side opposite the right angle) is not labeled with a length, but the angle adjacent to the base and the hypotenuse is marked with a question mark (?), indicating that this is the angle we need to find.
### Steps to Find the Missing Angle:
1. **Identify the Known Elements:**
- Base (adjacent side) = 38
- Height (opposite side) = 27
2. **Use Trigonometric Ratios:**
- Since we need to find the angle, we can use the tangent function, which is the ratio of the opposite side to the adjacent side.
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
\[
\tan(\theta) = \frac{27}{38}
\]
3. **Calculate the Angle:**
- Use the arctangent function (tan^(-1)) to find the angle.
\[
\theta = \tan^{-1}\left(\frac{27}{38}\right)
\]
- Calculate this value using a calculator or trigonometric tables.
By performing the calculation, students will find the value of the angle marked with the question mark. This method demonstrates practical usage of trigonometric functions in solving right triangle problems.
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