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Chapter 8: Q. 4 (page 555)

In Problems 3–5, use the given information to determine the three remaining parts of each triangle.

Short Answer

Expert verified

The missing values are $c = 16.3, C = 117 °, b = 6.85$

Step by step solution

01

Step 1. Given information

The given triangle is

02

Step 2. Use the rule of sines

According to the rule of sines, $\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$ .
Substitute $A = 41 °, a = 12, B = 22 °$ and solve to find the value of b.

$\begin{array}{rcl} \frac{\sin 41}{12} & = & \frac{\sin 22}{b} \\ b & = & 12 \frac{\sin 22}{\sin 41} \\ \approx & 6.85 \end{array}$

03

Step 3. Use the angle sun property

The sum of angles of a triangle is $180 °$
So, $\begin{array}{rcl} C & = & 180 ° - 41 ° - 22 ° \\ = & 117 ° \end{array}$

04

Step 4. use the rule of Sines

Use the rule of sines again and substitute $A = 41, a = 12, C = 117$ and solve to find c.

$\begin{array}{rcl} \frac{\sin 41}{12} & = & \frac{\sin 117}{c} \\ c & = & 12 \frac{\sin 117}{\sin 41} \\ \approx & 16.3 \end{array}$

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Most popular questions from this chapter

Solve each triangle.

$a = 10, b = 8, c = 5$

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