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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
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.
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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