Question

How do you solve a triangle ABC given A=150 degrees, C= 20 degrees, a= 200?

Answer 1

the six elements of a triangle are:
Sides
`a=200`
`b=69.459`
`c=136.808`
Angles
`A=150`
`B=10`
`C=20`

Explanation:

Given:
Angle `A=150`
Angle `C=20`
Side `a=200`
To find
Angle `B`
We know that
`A+B+C=180`
Substituting fir A and C
`150+B+20=180`
`170+B=180`
`B=180-170`
Solving for B
`B=10`
Side b
`b/sinB=a/sinA`
`b=a(sinB/sinA)`
Substituting for A, B and a
`b=200(sin10/sin150)`
`b=69.459`
Side c
`c/sinC=a/sinA`
`c=a(sinC/sinA)`
Substituting for A, C and a
`c=200(sin20/sin150)`
`c=136.808`

Thus, the six elements of a triangle are:
Sides
`a=200`
`b=69.459`
`c=136.808`
Angles
`A=150`
`B=10`
`C=20`