Question

A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 12, respectively. The angle between A and C is `(pi)/8` and the angle between B and C is `(3pi)/8`. What is the area of the triangle?

Answer 1

The Area of the `Delta`=42sq. units.

Explanation:

We denote, by `hat(A,B)`, the angle btwn. sides `A, and, B`.

From Geometry, we know that, in any `Delta`

`hat(A,B)+hat(B,C)+hat(C,A)=pi`

`:. hat(A,B)+3pi/8+pi/8=pi rArr hat(A,B)=pi/2`.

Thus, given `Delta` is a right-triangle, and, sides `A` and `B,`

having lengths `7` and `12` resp. are at right angle.

Accordingly, the Area of the `Delta`=1/2712=42 sq. units.