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

1 Answer
Hriman · NJ
Mar 16, 2018

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"#

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