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?

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Answer 1 · 2016-08-26T19:59:15

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

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.

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(pi)/8 and the angle between B and C is (3pi)/8 (3pi)/8. What is the area of the triangle?