A triangle has sides A, B, and C. The angle between sides A and B is $pi/3$ and the angle between sides B and C is $pi/12$ . If side B has a length of 14, what is the area of the triangle?

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Answer 1 · 2016-03-25T13:21:57

Area $=22.740979141751" "$ square units

From the given:
Angles $A=pi/12=15^@$ and $C=pi/3=60^@$
Therefore $B=105^@$
but side $b=14$

We only need one side to solve for the Area.

By the sine law
$a/sin A=b/sin B$

$a=(b*sin A)/sin B$

$a=(14*sin 15^@)/sin 105^@$

$a=3.7512886940358$

Now we can use the formula for area:

Area $=1/2*a*b*sin C$
Area $=1/2*(3.7512886940358)*14*sin 60^@$

Area $=22.740979141751" "$ square units

God bless....I hope the explanation is useful.

A triangle has sides A, B, and C. The angle between sides A and B is pi/3pi/3 and the angle between sides B and C is pi/12pi/12. If side B has a length of 14, what is the area of the triangle?