The equation sin(25°) = 6. can be used to find the length What is the length of AB? Round to the nearest tenth. of AB. 19.3 in. O 21.3 in. O 23.5 in. O 68.0 in. 25° C 9 in. B.
The equation sin(25°) = 6. can be used to find the length What is the length of AB? Round to the nearest tenth. of AB. 19.3 in. O 21.3 in. O 23.5 in. O 68.0 in. 25° C 9 in. B.
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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![**Using Trigonometry to Find the Length of a Right Triangle Side**
**Problem Statement:**
The equation \(\sin(25^\circ) = \frac{9}{c}\) can be used to find the length of \( \overline{AB} \).
**Diagram Explanation:**
A right triangle \( \triangle ABC \) is shown, where:
- \( \angle A \) is \( 25^\circ \)
- \( \overline{BC} \) (adjacent side to \( \angle A \)) is \( 9\, \text{in.} \)
- \( \overline{AB} \) (opposite side to \( \angle C \), which is \( 90^\circ \))
- The hypotenuse is labeled as \( c \)
**Question:**
What is the length of \( \overline{AB} \)? Round to the nearest tenth.
**Options:**
A) 19.3 in.
B) 21.3 in.
C) 23.5 in.
D) 68.0 in.
**Solution:**
To find the length of \( \overline{AB} \), we start with the given trigonometric equation:
\[ \sin(25^\circ) = \frac{9}{c} \]
We can isolate \( c \) (the hypotenuse) by multiplying both sides by \( c \):
\[ c \cdot \sin(25^\circ) = 9 \]
Next, divide both sides by \( \sin(25^\circ) \):
\[ c = \frac{9}{\sin(25^\circ)} \]
Using a calculator to find \( \sin(25^\circ) \):
\[ \sin(25^\circ) \approx 0.4226 \]
So,
\[ c = \frac{9}{0.4226} \approx 21.3 \]
Thus, the length of \( \overline{AB} \) is \( 21.3 \, \text{in.} \)
**Answer:**
B) 21.3 in.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fefc4e4-0fc1-4d3a-92e0-1dd9cbc9acda%2Fddf1a745-38c7-411c-9055-5896a9b7e3af%2Fsg3ikb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Using Trigonometry to Find the Length of a Right Triangle Side**
**Problem Statement:**
The equation \(\sin(25^\circ) = \frac{9}{c}\) can be used to find the length of \( \overline{AB} \).
**Diagram Explanation:**
A right triangle \( \triangle ABC \) is shown, where:
- \( \angle A \) is \( 25^\circ \)
- \( \overline{BC} \) (adjacent side to \( \angle A \)) is \( 9\, \text{in.} \)
- \( \overline{AB} \) (opposite side to \( \angle C \), which is \( 90^\circ \))
- The hypotenuse is labeled as \( c \)
**Question:**
What is the length of \( \overline{AB} \)? Round to the nearest tenth.
**Options:**
A) 19.3 in.
B) 21.3 in.
C) 23.5 in.
D) 68.0 in.
**Solution:**
To find the length of \( \overline{AB} \), we start with the given trigonometric equation:
\[ \sin(25^\circ) = \frac{9}{c} \]
We can isolate \( c \) (the hypotenuse) by multiplying both sides by \( c \):
\[ c \cdot \sin(25^\circ) = 9 \]
Next, divide both sides by \( \sin(25^\circ) \):
\[ c = \frac{9}{\sin(25^\circ)} \]
Using a calculator to find \( \sin(25^\circ) \):
\[ \sin(25^\circ) \approx 0.4226 \]
So,
\[ c = \frac{9}{0.4226} \approx 21.3 \]
Thus, the length of \( \overline{AB} \) is \( 21.3 \, \text{in.} \)
**Answer:**
B) 21.3 in.
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