Chapter 8: Q. 8 (page 555)

In Problems 6–8, solve each triangle.
$a = 8, b = 4, C = 70 °$

Short Answer

Expert verified

The missing values are $A = 80.59 °, B = 29.55 °, c = 7.62$ .

Step by step solution

Step 1. Given information

The given values are $a = 8, b = 4, C = 70 °$ .

Step 2. Use the rule of cosines

According to the rule of cosines, $c^{2} = a^{2} + b^{2} - 2 a b \cos C$ .
Substitute the given values into the equation and find the length c.

$\begin{array}{rcl} c^{2} & = & 4^{2} + 8^{2} - 2 (4) (8) \cos 70 \\ = & 16 + 64 - 21.89 \\ \approx & 58.11 \\ c & \approx & 7.62 \end{array}$

Step 3. Use the rule of Sines

Substitute $a = 8, b = 4, C = 70 °, c = 7.62$ into the rule of sine equation and solve for A, B.

$\begin{array}{rcl} \frac{\sin A}{8} & = & \frac{\sin B}{4} = \frac{\sin 70}{7.62} \\ \sin A & = & 8 \frac{\sin 70}{7.62} \\ A & \approx & 80.59 ° \\ \sin B & = & 4 \frac{\sin 70}{7.62} \\ \approx & 29.55 ° \end{array}$

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In Problems 6–8, solve each triangle.
$a = 8, b = 4, C = 70 °$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Use the rule of cosines

Step 3. Use the rule of Sines

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In Problems 6–8, solve each triangle.a=8,b=4,C=70°

Short Answer

Step by step solution

Step 1. Given information

Step 2. Use the rule of cosines

Step 3. Use the rule of Sines

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Statistics

Decision Maths

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 6–8, solve each triangle.
$a = 8, b = 4, C = 70 °$