Question

How do you solve the triangle given `B=15^circ30', a=4.5, b=6.8`?

Answer 1

`color(blue)("Area of Triangle " A_t = 6.63" sq units"`

Explanation:

`hat B = 15.5^@, a = 4.5, b = 6.8`

Applying the law of sines,

`sin A = (sin B * a) / b = (sin (15.5) * 4.5) / 6.8 = 0.1768`

`hat A = sin ^_1 0.1768 = 10.18^@`

`hat C = 180 - hat A - hat B = 180 - 10.18 - 15.5 = 154.32^@`

`"Area of Triangle " A_t = (1/2) a b sin C = (1/2) * 4.5 * 6.8 * sin 154.32 = 6.63" sq units"`