Question

State the number of possible triangles that can be formed using the given measurements? C= 52°, b= 31km, c= 30km

Answer 1

Two triangles

Explanation:

There is a chance that this could be an ambiguous case. As we have a Side, Side, Angle we could either form two triangles, one triangle or no triangle.

We have a match pair so let's use law of sines:
`\angleB_1`= `arcsin((sin(52^o)(31))/30)= 54.516^o`

Now there could be another triangle, so let's test for that possibility:
`\angleB_2`= `180^o-54.516^o= 125.484^o`

Now that we know that there's two possible triangles:
`\angleC_1`= `180^o-52^o-54.516^o= 73.484^o`
`\angleC_2`= `180^o-52^o-125.484^o= 2.516^o`

Now for each of side `\angleC`:
`c_1`= `(30sin(73.484^o))/sin(52^o)= 36.5 " km"`
`c_2`= `(30sin(2.516^o))/sin(52^o)= 1.67 " km"`