A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 7, respectively. The angle between A and C is 13π24 and the angle between B and C is π8. What is the area of the triangle?

1 Answer
Ratnaker Mehta
Jul 14, 2016

Area of the triangle=7√3≅12.1247sq.unit.

Explanation:

We note that the third angle of the triangle =π−13π24−π8=(24−13−3)π24=8π24=π3.

This is the angle btwn. sides A&B

Now, by Trigo., area of the triangle=12⋅A⋅B⋅sin(∠(A,B)
=12⋅4⋅7⋅sin(π3)=12⋅4⋅7⋅√32=7√3≅7⋅(1.7321)=12.1247 sq.unit.

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