A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{π}{2}$ $(pi)/2$ , the angle between sides B and C is $\frac{π}{3}$ $pi/3$ , and the length of B is 8, what is the area of the triangle?

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Answer 1 · 2017-01-01T10:37:56

The area of the triangle is $55.43 (2 d p)$ $55.43(2dp)$ sq.unit

The angle between sides $A and B$ $A and B$ is $∠ c = \frac{π}{2} = \frac{180}{2} = 90^{0}$ $/_c=pi/2=180/2=90^0$

The angle between sides $B and C$ $B and C$ is $∠ a = \frac{π}{3} = \frac{180}{3} = 60^{0}$ $/_a=pi/3=180/3=60^0$

This is a right triangle with base $B=8 :. tan a = A/B or A= B *tana :. A = 8 *tan60 =8*sqrt3$

The area of the triangle is $A_t= 1/2 * B* A= 1/2*8*8*sqrt3 = 32* sqrt3=55.43(2dp)$ sq.unit [Ans]

A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/2π2(pi)/2, the angle between sides B and C is pi/3π3pi/3, and the length of B is 8, what is the area of the triangle?