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B 25 C C b=? O b = 2.33 O b = 5.33 Ob = 4.33 O b = 3.33

B 25 C C b=? O b = 2.33 O b = 5.33 Ob = 4.33 O b = 3.33

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 Side \( b \) in a Right Triangle #### Problem Description: We have a right triangle \( \triangle ABC \) where: - ∠C is a right angle (90°), - The length of side \( BC \) is 5 units, - ∠B is 25°, - We need to find the length of side \( b = AC \). The options are: - \( b = 2.33 \) - \( b = 5.33 \) - \( b = 4.33 \) - \( b = 3.33 \) #### Diagram Explanation: - \( \triangle ABC \) has a right angle at \( C \), - Side \( BC \) is perpendicular to side \( AC \), - The length of side \( BC \) is given as 5 units, - ∠B measures 25°, - We need to determine the length of side \( b \) (AC). ### Solution: Given: - \( \angle B = 25° \) - \( BC = 5 \) (adjacent side to angle \( B \)) We use the tangent function, which relates an angle to the ratio of the opposite side over the adjacent side in a right triangle: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] Here: \[ \tan(25°) = \frac{b}{5} \] Solving for \( b \): \[ b = 5 \cdot \tan(25°) \] Using a calculator to find \( \tan(25°) \approx 0.4663 \), \[ b \approx 5 \cdot 0.4663 \approx 2.33 \] Thus, the length of side \( b (AC) \) is approximately 2.33 units. ### Conclusion: The correct length of side \( b \) is: \[ \boxed{b = 2.33} \] Feel free to reach out if you have any questions or need further clarification!
Transcribed Image Text:### Finding the Length of Side \( b \) in a Right Triangle #### Problem Description: We have a right triangle \( \triangle ABC \) where: - ∠C is a right angle (90°), - The length of side \( BC \) is 5 units, - ∠B is 25°, - We need to find the length of side \( b = AC \). The options are: - \( b = 2.33 \) - \( b = 5.33 \) - \( b = 4.33 \) - \( b = 3.33 \) #### Diagram Explanation: - \( \triangle ABC \) has a right angle at \( C \), - Side \( BC \) is perpendicular to side \( AC \), - The length of side \( BC \) is given as 5 units, - ∠B measures 25°, - We need to determine the length of side \( b \) (AC). ### Solution: Given: - \( \angle B = 25° \) - \( BC = 5 \) (adjacent side to angle \( B \)) We use the tangent function, which relates an angle to the ratio of the opposite side over the adjacent side in a right triangle: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] Here: \[ \tan(25°) = \frac{b}{5} \] Solving for \( b \): \[ b = 5 \cdot \tan(25°) \] Using a calculator to find \( \tan(25°) \approx 0.4663 \), \[ b \approx 5 \cdot 0.4663 \approx 2.33 \] Thus, the length of side \( b (AC) \) is approximately 2.33 units. ### Conclusion: The correct length of side \( b \) is: \[ \boxed{b = 2.33} \] Feel free to reach out if you have any questions or need further clarification!
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