Question

Solve for the remaining angles and side of the two triangles that can be created. Round to the nearest hundredth: B=30°, b=4, a=6 g

Answer 1

Answer:

A=48.59°, C=101.41°,c=7.84

Step-by-step explanation:

B=30°, b=4, a=6

Apply sine law to solve the triangle

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

$\frac{Sin A}{6} =\frac{Sin 30}{4}$

cross multiply it

$sin A=6 \cdot \frac{Sin 30}{4}$

$A=sin^{-1}6 \cdot \frac{Sin 30}{4}$

A=48.59°

sum of angles = 180 degree

angle C= 180 - angle A - angle B

$C= 180-30-48.59=101.41$

C=101.41°

$\frac{Sin B}{b} =\frac{Sin C}{c}$

$\frac{Sin 30}{4} =\frac{Sin 101.41}{c}$

Cross multiply

$c sin(30)= 4sin(101.41)$

divide both sides by sin(30)

c=7.84