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

`(a)/(sinA)=(c)/(sinC)`

substitute given values

`(a)/(s\imaginaryI n45^o)=(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

`(b)/(s\imaginaryI nB)=(c)/(s\imaginaryI nC)`

substitute given values

`(b)/(s\imaginaryI n35^o)=(3)/(s\imaginaryI n100^o)`
`b=\frac{3*s\mathrm{i}n35^o}{s\imaginaryI n100^o}`

b=1.75 units