Question

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?

Answer 1

Area`=22.740979141751" "`square units

Explanation:

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.