Answer to Question #142865 in Trigonometry for Raffy

Question

Solve the following triangles. Identify the case # in each given
triangle.

3.) Given parts:

a= 4 b= 8 A=30°

Answer 1

A=30$\degree$ , a=4 , b=8

step 1. use the law of cosines to find the side

c² = b² + a² -2ba cosA

c² = 8² + 4² - 2(8)(4) cos30$\degree$

c²= 64 + 16 + 64 (0.86)

c² = 80 + 55.04

c² = 135

c = 11.61

step 2. use the law of sin to find the opposite angle

$\frac{b}{sinB}$ = $\frac{a}{sinA}$

$\frac{8}{SinB}$ = $\frac{4}{sin30}$

4sinB =8sin30$\degree$

sinB = 2 sin30$\degree$

sinB = 1

B = 90$\degree$

step 3. find the third angle

C = 180$\degree$ - A - B

C = 180$\degree$ - 30$\degree$ - 90$\degree$

C = 60$\degree$

the solution is C= 60$\degree$ B = 90$\degree$ and c = 11.61