A triangle has sides A,B, and C. If the angle between sides A and B is $(pi)/2$ , the angle between sides B and C is $pi/6$ , and the length of B is 18, what is the area of the triangle?

Question

1576 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-26T01:26:22

Area of triangle $color(crimson)(A_t = 93.51$ sq units

$b = 18, hat A = pi/6, hat C = pi/2$

$hat B = pi - pi/6 - pi/2 = pi/3$

It’s a right triangle.

As per Law of Sines,

$a = (b sin A)/ sin B$

$a = (18 * sin (pi/6) )/ sin (pi/3) = 10.38$

Area of triangle $A_t = (1/2) a b sin C$

$A_t = (1/2) * 10.39 * 18 * sin (pi/2) = 93.51$

A triangle has sides A,B, and C. If the angle between sides A and B is (pi)/2(pi)/2, the angle between sides B and C is pi/6pi/6, and the length of B is 18, what is the area of the triangle?