Lloyd's work to find the missing angle measure (to the nearest degree) is shown. What mistake did Lloyd make? 9 units Lloyd's work: = X COS = 1° COS ܙܩ ܩ ܙܩ 5 units X
Lloyd's work to find the missing angle measure (to the nearest degree) is shown. What mistake did Lloyd make? 9 units Lloyd's work: = X COS = 1° COS ܙܩ ܩ ܙܩ 5 units X
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter3: Radian Measure
Section3.4: Arc Length And Area Of A Sector
Problem 66PS
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![### Finding the Missing Angle of a Right Triangle (Example Problem)
Lloyd's attempt to find the missing angle measure (to the nearest degree) is shown. Review his work and identify the mistake he made.
#### Lloyd's Work:
```
cos (5/9) = x
cos (5/9) = 1°
```
#### Diagram:
We are given a right triangle where:
- The hypotenuse is 9 units.
- The adjacent side to the angle \( x \) is 5 units.
#### Analysis:
Lloyd is attempting to use the cosine function, which is defined as:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Given:
\[ \cos(x) = \frac{5}{9} \]
The correct method to find the angle \( x \) is to use the inverse cosine (arccos) function:
\[ x = \cos^{-1}\left(\frac{5}{9}\right) \]
#### Mistake Identified:
Lloyd did not actually use the inverse cosine function (cosine inverse or arccos). Instead, he incorrectly interpreted \( \cos (5/9) \) as an angle measure, which is not mathematically appropriate.
Moreover, cosine values must always be between -1 and 1, and thus the cosine of a ratio like 5/9 should not yield an angle directly.
#### Corrected Work:
Apply the inverse cosine to find the angle \( x \):
\[ x = \cos^{-1}\left(\frac{5}{9}\right) \]
Using a calculator:
\[ x \approx \cos^{-1}(0.5556) \approx 56 \text{ degrees} \]
#### Conclusion:
Lloyd's mistake was not applying the inverse cosine function to find the angle. The correct measure of angle \( x \) is approximately 56 degrees.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f3e5dad-3eef-4af4-8432-92621aeb9e2a%2F376a493d-4067-4798-a461-21af2acc1a7c%2Flbmhqfd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Missing Angle of a Right Triangle (Example Problem)
Lloyd's attempt to find the missing angle measure (to the nearest degree) is shown. Review his work and identify the mistake he made.
#### Lloyd's Work:
```
cos (5/9) = x
cos (5/9) = 1°
```
#### Diagram:
We are given a right triangle where:
- The hypotenuse is 9 units.
- The adjacent side to the angle \( x \) is 5 units.
#### Analysis:
Lloyd is attempting to use the cosine function, which is defined as:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Given:
\[ \cos(x) = \frac{5}{9} \]
The correct method to find the angle \( x \) is to use the inverse cosine (arccos) function:
\[ x = \cos^{-1}\left(\frac{5}{9}\right) \]
#### Mistake Identified:
Lloyd did not actually use the inverse cosine function (cosine inverse or arccos). Instead, he incorrectly interpreted \( \cos (5/9) \) as an angle measure, which is not mathematically appropriate.
Moreover, cosine values must always be between -1 and 1, and thus the cosine of a ratio like 5/9 should not yield an angle directly.
#### Corrected Work:
Apply the inverse cosine to find the angle \( x \):
\[ x = \cos^{-1}\left(\frac{5}{9}\right) \]
Using a calculator:
\[ x \approx \cos^{-1}(0.5556) \approx 56 \text{ degrees} \]
#### Conclusion:
Lloyd's mistake was not applying the inverse cosine function to find the angle. The correct measure of angle \( x \) is approximately 56 degrees.
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