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In the figure to the right c= 12 what is the measure of b? 30 (A) 6 (B) 63 (C) 12/3 (D) 24 (E) None of these

In the figure to the right c= 12 what is the measure of b? 30 (A) 6 (B) 63 (C) 12/3 (D) 24 (E) None of these

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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### Problem Statement In the figure to the right, \(c = 12\). What is the measure of \(b\)? - (A) 6 - (B) \(6\sqrt{3}\) - (C) \(12\sqrt{3}\) - (D) 24 - (E) None of these ### Diagram The figure shows a right triangle with a hypotenuse \(c = 12\), an angle of 30 degrees, and sides labeled \(a\) and \(b\). The right angle is between \(a\) and \(b\). ### Tips Use trigonometric ratios and then determine which answer matches decimal. ### Tools to Help You For the triangle below: ``` /| / | h / | / | y /θ___| x ``` - \(\tan \theta = \frac{\text{opposite leg}}{\text{adjacent leg}} = \frac{y}{x}\) - \(\sin \theta = \frac{\text{opposite leg}}{\text{hypotenuse}} = \frac{y}{h}\) - \(\cos \theta = \frac{\text{adjacent leg}}{\text{hypotenuse}} = \frac{x}{h}\) Also for the triangle above, from the Pythagorean Theorem: \(h^2 = x^2 + y^2\). ### Answer Choices - (A) 6 - (B) \(6\sqrt{3}\) - (C) \(12\sqrt{3}\) - (D) 24 - (E) None of these
Transcribed Image Text:### Problem Statement In the figure to the right, \(c = 12\). What is the measure of \(b\)? - (A) 6 - (B) \(6\sqrt{3}\) - (C) \(12\sqrt{3}\) - (D) 24 - (E) None of these ### Diagram The figure shows a right triangle with a hypotenuse \(c = 12\), an angle of 30 degrees, and sides labeled \(a\) and \(b\). The right angle is between \(a\) and \(b\). ### Tips Use trigonometric ratios and then determine which answer matches decimal. ### Tools to Help You For the triangle below: ``` /| / | h / | / | y /θ___| x ``` - \(\tan \theta = \frac{\text{opposite leg}}{\text{adjacent leg}} = \frac{y}{x}\) - \(\sin \theta = \frac{\text{opposite leg}}{\text{hypotenuse}} = \frac{y}{h}\) - \(\cos \theta = \frac{\text{adjacent leg}}{\text{hypotenuse}} = \frac{x}{h}\) Also for the triangle above, from the Pythagorean Theorem: \(h^2 = x^2 + y^2\). ### Answer Choices - (A) 6 - (B) \(6\sqrt{3}\) - (C) \(12\sqrt{3}\) - (D) 24 - (E) None of these
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