Which inverse trigonometric function must you use to calculate the measure of angle C? 9. 40 Note: Figure is not drawn to scale
Which inverse trigonometric function must you use to calculate the measure of angle C? 9. 40 Note: Figure is not drawn to scale
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter2: Right Triangle Trigonometry
Section: Chapter Questions
Problem 5GP
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![**Educational Content: Calculating Angle using Inverse Trigonometric Functions**
**Question:**
Which inverse trigonometric function must you use to calculate the measure of angle \( C \)?
**Diagram Explanation:**
There is a right-angled triangle \( \triangle SBC \) depicted, where:
- \( \angle SBC \) is the right angle (90 degrees).
- The length \( SB \) (opposite to angle \( C \)) is given as 9 units.
- The length \( BC \) (adjacent to angle \( C \)) is given as 40 units.
- Note: The given figure is not drawn to scale.
**Answer Options:**
- \( \text{o} \) sine
- \( \text{o} \) tangent
- \( \text{o} \) cosine
**Solution Approach:**
To find the measure of angle \( C \) in the right-angled triangle, we need to use an inverse trigonometric function.
The sine, cosine, and tangent functions relate the sides of a right triangle to its angles:
- Sine (\( \sin \)) relates the opposite side to the hypotenuse.
- Cosine (\( \cos \)) relates the adjacent side to the hypotenuse.
- Tangent (\( \tan \)) relates the opposite side to the adjacent side.
Given:
- Opposite side (\( SB \)) = 9 units
- Adjacent side (\( BC \)) = 40 units
We use the tangent function because it directly involves the opposite and adjacent sides:
\[ \tan(C) = \frac{\text{opposite}}{\text{adjacent}} = \frac{9}{40} \]
To find the angle \( C \), we use the inverse tangent (\( \arctan \)) function:
\[ C = \arctan\left(\frac{9}{40}\right) \]
**Your answer:**
- \( \text{o} \) sine
- \( \text{●} \) tangent
- \( \text{o} \) cosine](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f64770f-f497-4deb-ade0-bee918e37a8e%2Fdfe68801-79c9-4e0c-a6fc-654697e7d9ce%2Fsilctfh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content: Calculating Angle using Inverse Trigonometric Functions**
**Question:**
Which inverse trigonometric function must you use to calculate the measure of angle \( C \)?
**Diagram Explanation:**
There is a right-angled triangle \( \triangle SBC \) depicted, where:
- \( \angle SBC \) is the right angle (90 degrees).
- The length \( SB \) (opposite to angle \( C \)) is given as 9 units.
- The length \( BC \) (adjacent to angle \( C \)) is given as 40 units.
- Note: The given figure is not drawn to scale.
**Answer Options:**
- \( \text{o} \) sine
- \( \text{o} \) tangent
- \( \text{o} \) cosine
**Solution Approach:**
To find the measure of angle \( C \) in the right-angled triangle, we need to use an inverse trigonometric function.
The sine, cosine, and tangent functions relate the sides of a right triangle to its angles:
- Sine (\( \sin \)) relates the opposite side to the hypotenuse.
- Cosine (\( \cos \)) relates the adjacent side to the hypotenuse.
- Tangent (\( \tan \)) relates the opposite side to the adjacent side.
Given:
- Opposite side (\( SB \)) = 9 units
- Adjacent side (\( BC \)) = 40 units
We use the tangent function because it directly involves the opposite and adjacent sides:
\[ \tan(C) = \frac{\text{opposite}}{\text{adjacent}} = \frac{9}{40} \]
To find the angle \( C \), we use the inverse tangent (\( \arctan \)) function:
\[ C = \arctan\left(\frac{9}{40}\right) \]
**Your answer:**
- \( \text{o} \) sine
- \( \text{●} \) tangent
- \( \text{o} \) cosine
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