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Which equation can be used to find the length of AC? A 10 in. 40° C B a (10)sin(40°) = AC O (10)cos(40°) = AC 10 = AC sin(40°) 10 = AC cos(40°)

Which equation can be used to find the length of AC? A 10 in. 40° C B a (10)sin(40°) = AC O (10)cos(40°) = AC 10 = AC sin(40°) 10 = AC cos(40°)

Elementary Geometry For College Students, 7e
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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### Finding the Length of AC in a Right Triangle **Question:** Which equation can be used to find the length of \( AC \)? **Diagram Explanation:** The diagram represents a right triangle \( \triangle ABC \) where: - \( \angle BCA \) is \( 90^\circ \). - \( \angle CAB \) is \( 40^\circ \). - The hypotenuse \( AB \) measures \( 10 \) inches. - Side \( AC \) (opposite \( \angle CAB \)) is labeled as \( b \). - Side \( BC \) (adjacent to \( \angle CAB \)) is labeled as \( a \). **Given Choices:** - ( ) \( 10 \sin(40^\circ) = AC \) - ( ) \( 10 \cos(40^\circ) = AC \) - ( ) \( \frac{10}{\sin(40^\circ)} = AC \) - ( ) \( \frac{10}{\cos(40^\circ)} = AC \) **Explanation:** To find the correct equation to determine the length of \( AC \), note that: - \( \sin(\theta) \) is defined as the ratio of the length of the side opposite to \( \theta \) over the hypotenuse. - \( \cos(\theta) \) is defined as the ratio of the length of the side adjacent to \( \theta \) over the hypotenuse. Thus, \[ \sin(40^\circ) = \frac{AC}{AB} = \frac{AC}{10} \] Solving for \( AC \): \[ AC = 10 \sin(40^\circ) \] Therefore, the answer is: - \( 10 \sin(40^\circ) = AC \) **Interactive Options:** - **Mark this and return** - **Save and Exit** - **Next** - **Submit**
Transcribed Image Text:### Finding the Length of AC in a Right Triangle **Question:** Which equation can be used to find the length of \( AC \)? **Diagram Explanation:** The diagram represents a right triangle \( \triangle ABC \) where: - \( \angle BCA \) is \( 90^\circ \). - \( \angle CAB \) is \( 40^\circ \). - The hypotenuse \( AB \) measures \( 10 \) inches. - Side \( AC \) (opposite \( \angle CAB \)) is labeled as \( b \). - Side \( BC \) (adjacent to \( \angle CAB \)) is labeled as \( a \). **Given Choices:** - ( ) \( 10 \sin(40^\circ) = AC \) - ( ) \( 10 \cos(40^\circ) = AC \) - ( ) \( \frac{10}{\sin(40^\circ)} = AC \) - ( ) \( \frac{10}{\cos(40^\circ)} = AC \) **Explanation:** To find the correct equation to determine the length of \( AC \), note that: - \( \sin(\theta) \) is defined as the ratio of the length of the side opposite to \( \theta \) over the hypotenuse. - \( \cos(\theta) \) is defined as the ratio of the length of the side adjacent to \( \theta \) over the hypotenuse. Thus, \[ \sin(40^\circ) = \frac{AC}{AB} = \frac{AC}{10} \] Solving for \( AC \): \[ AC = 10 \sin(40^\circ) \] Therefore, the answer is: - \( 10 \sin(40^\circ) = AC \) **Interactive Options:** - **Mark this and return** - **Save and Exit** - **Next** - **Submit**
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