Question

Determine whether the given information results in one triangle or two. a=6, b=2, A=20 degrees

Answer 1

Given:

a = 6

b = 2

A = 20 degrees

a.) Let's determine Angle B. Apply the Sine Law.

$\text{ }\frac{a}{S\text{ine A}}\text{ = }\frac{b}{S\text{ine B}}$$\text{ }\frac{6}{S\text{ine }20^{\circ}}\text{ = }\frac{2}{S\text{ine B}}$$\text{ Sine B = }\frac{(2)(Sine20^{\circ})}{6}\text{ = 0.11400671444}$$\text{ B = Sine}^{-1}(\text{0.11400671444)}$$\text{ B }\approx6.55^{\circ}$

b.) Let's find Angle C.

$\angle A\text{ + }\angle B\text{ + }\angle C=180^{\circ}$$20^{\circ}+6.55^{\circ}\text{ + }\angle C=180^{\circ}$$\angle C+26.55^{\circ}=180^{\circ}$$\angle C=180^{\circ}\text{ - }26.55^{\circ}$$\text{ }\angle C=153.45^{\circ}$

Therefore, the measure of Angle C is 153.45 degrees.

c.) Let's determine the length of side c. Apply the Sine Law.

$\text{ }\frac{6}{S\text{ine }20^{\circ}}\text{ = }\frac{c}{S\text{ine }153.45^{\circ}}$$c\text{ = }\frac{(6)(S\text{ine }153.45^{\circ})}{S\text{ine }20^{\circ}}$$c\text{ }\approx\text{ 7.84}$

In Summary, the information results in one triangle with the following details:

a = 6

b = 2

c = 7.84

A = 20 degrees

B = 6.55 degrees

C = 153.45 degress