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B 165 m 17° Give each side and angle measure rounded to the nearest whole number. mZB 73 :: 48 m :: 50° :: 63 m :: 73 : 158 m ... 17 of 25 answered PREV 17 18 19 20 21 22 NEXT ...

B 165 m 17° Give each side and angle measure rounded to the nearest whole number. mZB 73 :: 48 m :: 50° :: 63 m :: 73 : 158 m ... 17 of 25 answered PREV 17 18 19 20 21 22 NEXT ...

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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### Triangle Calculation #### Problem Description: Given the right triangle ABC, where: - \( AB \) is the hypotenuse, - \( AC \) and \( BC \) are the legs of the triangle, - The angle \( \angle CAB \) is \( 17^\circ \), - The length of the hypotenuse \( AB \) is 165 meters. #### Task: Calculate each side and angle measure rounded to the nearest whole number. #### Diagram: ``` Triangle ABC: - Hypotenuse (AB): 165 meters - Angle \( \angle CAB \): \( 17^\circ \) B /| / | 165m a / | / | A---b---C Given: \( a \) = ? \( b \) = ? \( \angle B \) = ? ``` #### Solution Steps: 1. Given \( \angle CAB = 17^\circ \) and \( AB = 165 \) meters. 2. Use trigonometric relationships for right triangles to find \( a \) and \( b \): - \( a = AB \times \sin(\angle CAB) \) - \( b = AB \times \cos(\angle CAB) \) 3. Use the angle sum property of the triangle to find \( \angle ABC \): - \( \angle ABC = 90^\circ - \angle CAB \) #### Calculations: - \( a \approx 165 \times \sin(17^\circ) \approx 165 \times 0.292 \approx 48 \) meters - \( b \approx 165 \times \cos(17^\circ) \approx 165 \times 0.956 \approx 158 \) meters - \( \angle ABC \approx 90^\circ - 17^\circ = 73^\circ \) #### Final Answers: - \( a \): 48 meters - \( b \): 158 meters - \( \angle B \): 73° Note: All measurements are rounded to the nearest whole number as specified in the problem statement. #### Interactive Elements: You can fill in the calculated values and check your answers: - \( a \) = - \( b \) = - \( m \angle B \) = 73° Make sure to understand the trigonometric relationships used to solve the right triangle.
Transcribed Image Text:### Triangle Calculation #### Problem Description: Given the right triangle ABC, where: - \( AB \) is the hypotenuse, - \( AC \) and \( BC \) are the legs of the triangle, - The angle \( \angle CAB \) is \( 17^\circ \), - The length of the hypotenuse \( AB \) is 165 meters. #### Task: Calculate each side and angle measure rounded to the nearest whole number. #### Diagram: ``` Triangle ABC: - Hypotenuse (AB): 165 meters - Angle \( \angle CAB \): \( 17^\circ \) B /| / | 165m a / | / | A---b---C Given: \( a \) = ? \( b \) = ? \( \angle B \) = ? ``` #### Solution Steps: 1. Given \( \angle CAB = 17^\circ \) and \( AB = 165 \) meters. 2. Use trigonometric relationships for right triangles to find \( a \) and \( b \): - \( a = AB \times \sin(\angle CAB) \) - \( b = AB \times \cos(\angle CAB) \) 3. Use the angle sum property of the triangle to find \( \angle ABC \): - \( \angle ABC = 90^\circ - \angle CAB \) #### Calculations: - \( a \approx 165 \times \sin(17^\circ) \approx 165 \times 0.292 \approx 48 \) meters - \( b \approx 165 \times \cos(17^\circ) \approx 165 \times 0.956 \approx 158 \) meters - \( \angle ABC \approx 90^\circ - 17^\circ = 73^\circ \) #### Final Answers: - \( a \): 48 meters - \( b \): 158 meters - \( \angle B \): 73° Note: All measurements are rounded to the nearest whole number as specified in the problem statement. #### Interactive Elements: You can fill in the calculated values and check your answers: - \( a \) = - \( b \) = - \( m \angle B \) = 73° Make sure to understand the trigonometric relationships used to solve the right triangle.
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