Question

How do you solve the triangle ABC, given a=40, A=25, c=30?

Answer 1

`hatC = 18.5°," "hatB = 136.5° " and side " b = 65.2`

Explanation:

Angle A and side 'a' form a complete matching pair, so we can use the Sine rule to find angle C.
Angle A is opposite side 'a' and angle C is opposite side 'c'.

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

`(sin C)/30 = (sin 25)/40`

`sin C = (30sin25)/40 = 0.31696`

`hatC = 18.5°`

Now that we have two of the angles we can find the third angle from the sum of the angles in a triangle:

`hatB = 180°-25°-18.5° = 136.5°`

Use the Sine rule to find the length of side 'b'.

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

`b = (40sin136.5)/(sin25)`

`b= 65.2`