Chapter 8: Q. 6 (page 555)

In Problems 6–8, solve each triangle.
$A = 55 °, B = 20 °, a = 4$

Short Answer

Expert verified

The missing values are $C = 105 °, b = 9.58, c = 3.39$

Step by step solution

Step 1. Given information

The given values are $A = 55 °, B = 20 °, a = 4$ .

Step 2. Use the angle sum property

The sum of angles of a triangle is $180 °$ .
So,

$\begin{array}{rcl} C & = & 180 ° - 55 ° - 20 ° \\ = & 105 ° \end{array}$

Step 3. Use the rule of sines

Use the rule of sines $\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$ and substitute $A = 55, B = 20, C = 105, a = 4$ into the equation.
Solve the equation for b.

$\begin{array}{rcl} \frac{\sin 55}{4} & = & \frac{\sin 20}{b} \\ b & = & 4 \frac{\sin 55}{\sin 20} \\ \approx & 9.58 \end{array}$

Now, solve the equation for c.

$\begin{array}{rcl} \frac{\sin 55}{4} & = & \frac{\sin 105}{c} \\ c & = & 4 \frac{\sin 55}{\sin 105} \\ \approx & 3.39 \end{array}$

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In Problems 6–8, solve each triangle.
$A = 55 °, B = 20 °, a = 4$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Use the angle sum property

Step 3. Use the rule of sines

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In Problems 6–8, solve each triangle.A=55°,B=20°,a=4

Short Answer

Step by step solution

Step 1. Given information

Step 2. Use the angle sum property

Step 3. Use the rule of sines

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Pure Maths

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Problems 6–8, solve each triangle.
$A = 55 °, B = 20 °, a = 4$