A triangle has sides A, B, and C. Sides A and B have lengths of 9 and 4, respectively. The angle between A and C is $\frac{π}{12}$ $(pi)/12$ and the angle between B and C is $\frac{2 π}{3}$ $(2pi)/3$ . What is the area of the triangle?

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Answer 1 · 2016-10-02T10:09:30

Let angle beween A and C $= β = \frac{π}{12}$ $=beta=pi/12$

Angle beween B and C $= α = \frac{2 π}{3}$ $=alpha=(2pi)/3$

So angle beween A and B $= γ = π - \frac{π}{12} - \frac{2 π}{12} = \frac{π}{4}$ $=gamma=pi-pi/12-(2pi)/12=pi/4$

Again sides $A = 9 and B = 4$ $A=9 and B=4$

The area of the triangle

$Delta=1/2xxAxxBxxsingamma$

$=>Delta=1/2xx9xx4xxsin(pi/4)$

$=18xx1/sqrt2=9sqrt2squnit$

A triangle has sides A, B, and C. Sides A and B have lengths of 9 and 4, respectively. The angle between A and C is (pi)/12π12(pi)/12 and the angle between B and C is (2pi)/32π3 (2pi)/3. What is the area of the triangle?