A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 5, respectively. The angle between A and C is $\frac{5 π}{24}$ $(5pi)/24$ and the angle between B and C is $\frac{3 π}{8}$ $(3pi)/8$ . What is the area of the triangle?

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Answer 1 · 2017-11-18T11:03:06

Area of the triangle is $14.49$ $14.49$ sq.unit.

Angle between Sides $A and C$ $A and C$ is

$∠ b = \frac{5 π}{24} = \frac{5 \cdot 180}{24} = {37.5}^{0}$ $/_b= (5pi)/24=(5*180)/24=37.5^0$

Angle between Sides $B and C$ $B and C$ is

$/_a= (3pi)/8=(3*180)/8=67.5^0 :.$

Angle between Sides $A and B$ is

$/_c= 180-(37.5+67.5)=75^0$

Now we know sides $A=6 , B=5$ and their included angle

$/_c = 75^0$ . Area of the triangle is $A_t=(A*B*sinc)/2$

$:.A_t=(6*5*sin75)/2 ~~ 14.49$ sq.unit

Area of the triangle is $14.49$ sq.unit [Ans]

A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 5, respectively. The angle between A and C is (5pi)/245π24(5pi)/24 and the angle between B and C is (3pi)/83π8 (3pi)/8. What is the area of the triangle?