Question

Using the Law of Sines to find a triangle with one obtuse angle if A = 49 precent, a = 30, b = 33

Answer 1

B =
`56^(o)`

C =
`75^(o)`

c = 38

The given question can be solved using the sine rule which states that;

`(a)/(sin A)` =
`(b)/(sin B)` =
`(c)/(sin C)`

Given that;

A = 49 degrees, a = 30, and b = 33. Then.

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

`(30)/(sin 49^(o) )` =
`(33)/(sin B)`

sin B = 0.8302

B =
`Sin^(-1)` 0.8302

= 56.12

B =
`56^(o)`

But,

A + B + C = 180

49 + 56 + C = 180

C = 180 - 105

= 75

C =
`75^(o)`

Then,

`(a)/(sin A)` =
`(c)/(sin C)`

`(30)/(sin 49^(o) )` =
`(c)/(sin 75^(o) )`

c = 38.396

c = 38