Question

Using the law of sines, determine whether the given information results in one triangle, two triangle or no triangle at all. Solve any triangle that results. a=8angle B = 57 degreeAngle A =49 degree

Answer 1

step 1

Find out the measure of angle C

Remember that

In any triangle, the sum of the interior angles must be equal to 180 degrees

so

A+B+C=180 degrees

substitute given values

49+57+C=180

C=180-106

C=74 degrees

step 2

Find out the length side b

Applying the law of sines

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

substitute

`(8)/(s\imaginaryI n49^o)=(b)/(s\imaginaryI n57^o)`

Solve for b

`\begin{gathered} b=\frac{8*s\mathrm{i}n57^o}{s\imaginaryI n49^o} \\ \\ b=8.89\text{ ---> rounded to two decimal places} \end{gathered}`

step 3

Find out the length side c

Applying the law of sines

`(a)/(s\imaginaryI nA)=(c)/(s\imaginaryI nC)`

substitute

`(8)/(s\imaginaryI n49^o)=(c)/(s\imaginaryI n74^o)`

solve for c

`\begin{gathered} c=\frac{8*s\mathrm{i}n74^o}{s\imaginaryI n49^o} \\ \\ c=10.19\text{ ----> rounded to two decimal places} \end{gathered}`

therefore

N of triangles is only one

b=8.89

c=10.19

C=74 degrees