Question

Give clear and complete answers to the following problems and questions. Write your explanations clearly using complete sentences. Include diagrams whenever appropriate. Suppose that $a=5, b=10,$ and $\angle C=135^{\circ}$ in triangle $\triangle A B C .$ Find the third side $c .$

Name: Problem 11, Chapter 13: College Geometry
Uploaded: 2020-06-03T00:05:46-08:00
Duration: 1 min 24 s
Channel: Melissa Salvador
Description: Give clear and complete answers to the following problems and questions. Write your explanations clearly using complete sentences. Include diagrams whenever appropriate. Suppose that a=5, b=10, and ∠C=135^∘ in triangle A B C . Find the third side c .

   Give clear and complete answers to the following problems and questions. Write your explanations clearly using complete sentences. Include diagrams whenever appropriate.
Suppose that $a=5, b=10,$ and $\angle C=135^{\circ}$ in triangle $\triangle A B C .$ Find the third side $c .$

College Geometry

Barbara E.… 1st Edition

Chapter 13, Problem 11

Instant Answer

Solved by Expert Melissa Salvador

06/03/2020

Step 1

We know that side $a$ is 5, side $b$ is 10, and $\angle C$ is 135 degrees. We can represent this information on a triangle as shown below: \[ \begin{array}{c} Show more…

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Give clear and complete answers to the following problems and questions. Write your explanations clearly using complete sentences. Include diagrams whenever appropriate. Suppose that $a=5, b=10,$ and $\angle C=135^{\circ}$ in triangle $\triangle A B C .$ Find the third side $c .$

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Key Concepts

Triangle Geometry

Triangle geometry encompasses the study of relationships between the sides and angles of triangles. This field includes key theorems like the Law of Cosines, which provide systematic methods for solving various types of triangles, irrespective of whether they are right-angled or oblique.

Law of Cosines

The Law of Cosines is a fundamental principle in trigonometry that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is used to calculate an unknown side or angle when other sides and angles are known, generalizing the Pythagorean theorem to non-right triangles.

Trigonometric Functions

Trigonometric functions, such as cosine, are essential in linking angles to side lengths in triangles. They allow us to evaluate relationships within triangles, facilitating the computation of unknown values using known angles and sides.

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