Question

Solve for the remaining angle and sides of the triangle described below. Round to the nearest hundredth:C = 100°, A = 45°, c = 3

Answer 1

step 1

Find out the measure of angle B

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

A+B+C=180 degrees

substitute given values

45+B+100=180

B=180-145

B=35 degrees

step 2

Find out the length of the side a

Applying the law of sines

$\frac{a}{sinA}=\frac{c}{sinC}$

substitute given values

$\frac{a}{s\imaginaryI n45^o}=\frac{3}{s\imaginaryI n100^o}$$a=\frac{3*s\mathrm{i}n45^o}{s\imaginaryI n100^o}$

a=2.15 units

step 3

Find out the length of the side b

applying the law of sines

$\frac{b}{s\imaginaryI nB}=\frac{c}{s\imaginaryI nC}$

substitute given values

$\frac{b}{s\imaginaryI n35^o}=\frac{3}{s\imaginaryI n100^o}$$b=\frac{3*s\mathrm{i}n35^o}{s\imaginaryI n100^o}$

b=1.75 units