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Solve the triangle: 1. A B 18 112° 53° C

Solve the triangle: 1. A B 18 112° 53° C

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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**Solve the Triangle:** 1. Triangle ABC - Angle at vertex A is \(53^\circ\). - Angle at vertex B is \(112^\circ\). - Side AB is 18 units. The task is to find the unknown angles and sides of triangle ABC using the given information. ### Explanation: - **Vertices and Angles**: The triangle is labeled with vertices A, B, and C. Angle A is \(53^\circ\) and angle B is \(112^\circ\). - **Side Lengths**: The length of side AB is given as 18 units. To solve the triangle, you can use the following methods: 1. **Finding the Missing Angle**: Use the angle sum property of triangles. The sum of all angles in a triangle is \(180^\circ\). Therefore, angle C can be found by subtracting the sum of angles A and B from \(180^\circ\). 2. **Law of Sines or Law of Cosines**: These can be used to find the unknown sides AC and BC once angle C is determined.
Transcribed Image Text:**Solve the Triangle:** 1. Triangle ABC - Angle at vertex A is \(53^\circ\). - Angle at vertex B is \(112^\circ\). - Side AB is 18 units. The task is to find the unknown angles and sides of triangle ABC using the given information. ### Explanation: - **Vertices and Angles**: The triangle is labeled with vertices A, B, and C. Angle A is \(53^\circ\) and angle B is \(112^\circ\). - **Side Lengths**: The length of side AB is given as 18 units. To solve the triangle, you can use the following methods: 1. **Finding the Missing Angle**: Use the angle sum property of triangles. The sum of all angles in a triangle is \(180^\circ\). Therefore, angle C can be found by subtracting the sum of angles A and B from \(180^\circ\). 2. **Law of Sines or Law of Cosines**: These can be used to find the unknown sides AC and BC once angle C is determined.
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