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

Question

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

1 Answer

Impact of this question

2516 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-11T20:09:45

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

Explanation:

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

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

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question