A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 10, 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?

Question

1569 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-07T21:50:17

$S=35$

If $A/_C = pi/8$ and $B/_C = (3pi)/8$ then as the sum of the internal angles of a triangle always equals $pi$ , we have:

$A/_B = pi-pi/8-(3pi)/8 = pi-(4pi)/8 = pi-pi/2 = pi/2$

Thus this is a right triangle where $A$ and $B$ are the legs, and $C$ is the hypotenuse.

So the area of the triangle is:

$S = (A*B)/2 = (7*10)/2 = 70/2 = 35$

A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 10, 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?