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Chapter 6: Problem 68

Write an original problem that can be solved using the Law of sines. Then solve the problem.

Short Answer

Expert verified
The length of side BC is \(7\sqrt{6}/2\) units and the measure of angle C is 75 degrees.

Step by step solution

01

Formulate the Problem

Consider a triangle ABC, where angle A = 60 degrees, angle B = 45 degrees and the side opposite angle B (side AC) measures 7 units.
02

Apply the Law of Sines

To find the length of side BC (opposite to Angle A), we can set up the following equation based on the law of sines: \\ \(\frac{BC}{\sin A} = \frac{AC}{\sin B}\). Accordingly, \(\frac{BC}{\sin 60} = \frac{7}{\sin 45}\)
03

Solve for BC

By simplifying and isolating BC, \(\frac{BC}{\sqrt{3}/2} = \frac{7}{\sqrt{2}/2}\). Therefore, \(BC = \frac{7}{\sqrt{2}} \times \sqrt{3} = 7\sqrt{6}/2\) units
04

Solve for angle C

The sum of the angles in a triangle is 180 degrees. Thus, angle C can be found by subtracting the sum of angles A and B from 180 degrees. So, we have \(C = 180 - 60 - 45 = 75\) degrees

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