Q. 4 In Problems 3鈥�5, use the given... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 8: Q. 4 (page 555)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

The given triangle is

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 $A = 41 掳, a = 12, B = 22 掳$ and solve to find the value of b.

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

Step 3. Use the angle sun property

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

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.

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

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91影视

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Use the rule of sines

Step 3. Use the angle sun property

Step 4. use the rule of Sines

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