What is the measure of angle LKJ? Round to the (第) 8.9 = x can be used to find the 7.7 The equation tan- nearest whole degree. measure of angle LKJ. 41° 45° 49° 7.7 cm 8.9 cm 55°
What is the measure of angle LKJ? Round to the (第) 8.9 = x can be used to find the 7.7 The equation tan- nearest whole degree. measure of angle LKJ. 41° 45° 49° 7.7 cm 8.9 cm 55°
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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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.
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![### Measuring Angle LKJ Using Trigonometric Functions
#### Problem Statement
The equation \(\tan^{-1}\left(\frac{8.9}{7.7}\right) = x\) can be used to find the measure of angle \(LKJ\).
#### Triangle Diagram
A right triangle \(LKJ\) is shown:
- \(L\) is the right angle.
- The length of \(KL\) (adjacent to angle \(LKJ\)) is 7.7 cm.
- The length of \(LJ\) (opposite to angle \(LKJ\)) is 8.9 cm.
- The hypotenuse \(KJ\) is not labeled with a length.
#### Question
What is the measure of angle \(LKJ\)? Round to the nearest whole degree.
- \(41^\circ\)
- \(45^\circ\)
- \(49^\circ\)
- \(55^\circ\)
#### Explanation:
To find the measure of angle \(LKJ\), use the arctangent function, which is the inverse of the tangent function:
\[ \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right) = \tan^{-1}\left(\frac{8.9}{7.7}\right) \]
1. Calculate the value inside the inverse tangent function:
\[ \frac{8.9}{7.7} \approx 1.1558 \]
2. Find the arctangent of this value:
\[ \tan^{-1}(1.1558) \approx 49^\circ \]
Therefore, the measure of angle \(LKJ\), rounded to the nearest whole degree, is \(49^\circ\).
#### Multiple-Choice Answer
- The correct answer is \(49^\circ\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fefc4e4-0fc1-4d3a-92e0-1dd9cbc9acda%2F66d2face-e54a-4782-9aca-c1d789215806%2Fjpjocmq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Measuring Angle LKJ Using Trigonometric Functions
#### Problem Statement
The equation \(\tan^{-1}\left(\frac{8.9}{7.7}\right) = x\) can be used to find the measure of angle \(LKJ\).
#### Triangle Diagram
A right triangle \(LKJ\) is shown:
- \(L\) is the right angle.
- The length of \(KL\) (adjacent to angle \(LKJ\)) is 7.7 cm.
- The length of \(LJ\) (opposite to angle \(LKJ\)) is 8.9 cm.
- The hypotenuse \(KJ\) is not labeled with a length.
#### Question
What is the measure of angle \(LKJ\)? Round to the nearest whole degree.
- \(41^\circ\)
- \(45^\circ\)
- \(49^\circ\)
- \(55^\circ\)
#### Explanation:
To find the measure of angle \(LKJ\), use the arctangent function, which is the inverse of the tangent function:
\[ \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right) = \tan^{-1}\left(\frac{8.9}{7.7}\right) \]
1. Calculate the value inside the inverse tangent function:
\[ \frac{8.9}{7.7} \approx 1.1558 \]
2. Find the arctangent of this value:
\[ \tan^{-1}(1.1558) \approx 49^\circ \]
Therefore, the measure of angle \(LKJ\), rounded to the nearest whole degree, is \(49^\circ\).
#### Multiple-Choice Answer
- The correct answer is \(49^\circ\).
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