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Chapter 8: Q. 3 (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 $a = 18$ , $B \approx 48.09 °$ , and $C = 79.9 °$

Step by step solution

01

Step 1. Given information

The given triangle is

02

Step 2. Use the Rule of Cosines

By the rule of cosines, $a^{2} = b^{2} + c^{2} - 2 b c \cos A$
Substitute the values $b = 17, c = 19, A = 52 °$ to find the value of a.

$\begin{array}{rcl} a^{2} & = & 17^{2} + 19^{2} - 2 (17) (19) \cos (52) \\ \approx & 289 + 361 - 397.72 \\ \approx & 324.28 \\ a & \approx & 18 \end{array}$

03

Step 3. Use the rule of Sines

According to the rule of sines, $\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$ .
Substitute $b = 17, a = 18, A = 52 °$ into the formula and find the value of angle B.

$\begin{array}{rcl} \frac{\sin (52)}{18} & = & \frac{\sin B}{17} \\ \sin B & = & 17 \times \frac{0.788}{18} \\ B & \approx & 48.09 \end{array}$

04

Step 4. Use Angle sum Property

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

So, $\begin{array}{rcl} C & = & 180 ° - 52 ° - 48.09 ° \\ = & 79.9 ° \end{array}$

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Most popular questions from this chapter

Find an equation for the circle with center at the point $(- 5, 1)$ and radius 3. Graph this circle.

In the given problem solve the triangle using either the law of sines or law of cosines-

$a = 14, b = 7, A = 85 °$

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