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

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

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Answer 1 · 2018-02-11T20:09:45

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
$A=150$
$B=10$
$C=20$

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

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