Question

How do you use law of sines to solve the triangle given A=24 degrees, a=8.5, c=10.6?

Answer 1

`C = 30.5° and B = 125.5° and b = 17.0`

Explanation:

In order to use the Sine Rule you have to know the size of one angle and the length of its opposite side. A third measurement can be either another side or an angle.

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

We have angle A, and sides a and c.`rArr` we can find angle C.
I prefer to have the unknown at the top of the left side.

`sin C/10.6 = sin 24/8.5 " "rArr" " sin C = (10.6 xxsin 24)/8.5`

Note than Sin values are always from 0 to 1, so we are expecting an answer of 0....... If this does not happen there is an error.

`Sin C=0.5.722...." find arcsin, " (sin)^-1`

`:. C = 30.5°`

To solve the triangle means to find all the unknown sides and angles. We need to find angle B and side b

`"Angle B" = 180° - 24° - 30.5° = 125.5° " (angles in a triangle)"`

`b/sin 125.5 = 8.5/sin 24 " "rArr" " b = (8.5 xxsin 125.5)/sin 24`

`b = 17.0`