Question

Solve the triangle. A=42 degrees B=67 degrees a=15.What is C degrees=What is b=What is c=

Answer 1

we know that

A=42 degrees

B=67 degrees

a=15 units

step 1

Find out the measure of angle C

Remember that

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

so

A+B+C=180 degrees

substitute

42+67+C=180

C=180-109

C=71 degrees

step 2

Find out the measure of the side b

Applying the law of sines

`(a)/(sinA)=(b)/(sinB)`

substitute given values

`\begin{gathered} (15)/(s\imaginaryI n42^o)=(b)/(s\imaginaryI n67^o) \\ \\ b=\frac{15*s\mathrm{i}n67^o}{s\imaginaryI n42^o} \\ \\ b=20.6\text{ units} \end{gathered}`

step 3

Find out the measure of the side c

Applying the law of sines

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

substitute given values

`\begin{gathered} (15)/(s\imaginaryI n42^o)=(c)/(s\imaginaryI n71^o) \\ \\ c=\frac{15*s\mathrm{i}n71^o}{s\imaginaryI n42^o} \\ \\ c=21.2\text{ units} \end{gathered}`