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Which of the following equations could be used to find the height of the obtuse triangle shown? Select all that apply. A B h sin (180° - A) = h sin B = cos (180° ☐ A) = b h Osin A = cos A = h b h b

Which of the following equations could be used to find the height of the obtuse triangle shown? Select all that apply. A B h sin (180° - A) = h sin B = cos (180° ☐ A) = b h Osin A = cos A = h b h 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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Question
## Finding the Height of an Obtuse Triangle ### Problem Statement Which of the following equations could be used to find the height of the obtuse triangle shown? Select all that apply. ### Triangle Diagram The image depicts an obtuse triangle \( \triangle ABC \) with the following properties: - \( \angle A \) is acute, and the triangle extends such that \( \angle C \) is obtuse. - Side \( a \) is opposite to \( \angle A \), side \( b \) is opposite to \( \angle B \), and side \( c \) is opposite to \( \angle C \). - \( h \) is the height from vertex \( C \) perpendicular to the line extending from side \( AB \). ### Given Equations 1. \(\sin(180^\circ - A) = \frac{h}{b}\) 2. \(\sin B = \frac{h}{a}\) 3. \(\cos(180^\circ - A) = \frac{h}{b}\) 4. \(\sin A = \frac{h}{b}\) 5. \(\cos A = \frac{h}{b}\) ### Solution Explanation In order to find the height \( h \), you need to use trigonometric relationships involving the given angles and sides. - \(\sin(180^\circ - A) = \sin A\). Thus, \(\sin(180^\circ - A) = \frac{h}{b}\) can be rewritten as \(\sin A = \frac{h}{b}\), which matches one of the given equations. - The equation \(\sin B = \frac{h}{a}\) involves angle \( B \) and side \( a \), but for angle \( B \) to be usable it must be an angle in a different position relative to height \( h \). - \(\cos(180^\circ - A) = -\cos A\), typically can resolve into a different trigonometric relationship, and may not directly help in finding \( h \). ### Correct Options The correct equations that can be used to find the height \( h \) are: 1. \(\sin(180^\circ - A) = \frac{h}{b}\) 2. \(\sin A = \frac{h}{b}\) Both of these relationships can be simplified to form a
Transcribed Image Text:## Finding the Height of an Obtuse Triangle ### Problem Statement Which of the following equations could be used to find the height of the obtuse triangle shown? Select all that apply. ### Triangle Diagram The image depicts an obtuse triangle \( \triangle ABC \) with the following properties: - \( \angle A \) is acute, and the triangle extends such that \( \angle C \) is obtuse. - Side \( a \) is opposite to \( \angle A \), side \( b \) is opposite to \( \angle B \), and side \( c \) is opposite to \( \angle C \). - \( h \) is the height from vertex \( C \) perpendicular to the line extending from side \( AB \). ### Given Equations 1. \(\sin(180^\circ - A) = \frac{h}{b}\) 2. \(\sin B = \frac{h}{a}\) 3. \(\cos(180^\circ - A) = \frac{h}{b}\) 4. \(\sin A = \frac{h}{b}\) 5. \(\cos A = \frac{h}{b}\) ### Solution Explanation In order to find the height \( h \), you need to use trigonometric relationships involving the given angles and sides. - \(\sin(180^\circ - A) = \sin A\). Thus, \(\sin(180^\circ - A) = \frac{h}{b}\) can be rewritten as \(\sin A = \frac{h}{b}\), which matches one of the given equations. - The equation \(\sin B = \frac{h}{a}\) involves angle \( B \) and side \( a \), but for angle \( B \) to be usable it must be an angle in a different position relative to height \( h \). - \(\cos(180^\circ - A) = -\cos A\), typically can resolve into a different trigonometric relationship, and may not directly help in finding \( h \). ### Correct Options The correct equations that can be used to find the height \( h \) are: 1. \(\sin(180^\circ - A) = \frac{h}{b}\) 2. \(\sin A = \frac{h}{b}\) Both of these relationships can be simplified to form a
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