Question

Calculate the side lengths a and b to two decimal places

Answer 1

Answer:

A) a = 11.08 and b = 12.94

Step-by-step explanation:

We will use the law of sines to answer this problem.

First we find the measure of the missing angle.  The sum of the measures of the angles of a triangle is 180°.  The two given angles are 58 and 82; this gives us 58+82 = 140°.  This leaves the third angle as 180-140 = 40°.

The law of sines is

$\frac{\sin{A}}{a}=\frac{\sin{B}}{b}=\frac{\sin{C}}{c}$

We have the measures of ∠C and side c; this makes the first ratio in our proportion

$\frac{\sin{40}}{8.4}$

To find the measure of side a, our proportion will be

$\frac{\sin{40}}{8.4}=\frac{\sin{58}}{a}$

Cross multiplying, we have

a(sin 40) = 8.4(sin 58)

Divide both sides by (sin 40):

a(sin 40)/(sin 40) = 8.4(sin 58)/(sin 40)

a = 11.08

To find the length of side b, we use our original ratio

$\frac{\sin{40}}{8.4}$

and the proportion

$\frac{\sin{40}}{8.4}=\frac{\sin{82}}{b}$

Cross multiplying,

b(sin 40) = 8.4(sin 82)

Divide both sides by (sin 40):

b(sin 40)/(sin 40) = 8.4(sin 82)/(sin 40)

b = 12.94

Answer 2

The answer is A. 

a= 11.08 and b= 12.94