How many distinct triangles can be formed for which m∠x = 51°, x = 5, and y = 2? zero one two

From the law of sines, we have:

, 

where x and y are the sides opposite to angles X and Y, respectively.

Substituting the known values, we have:

, thus

                           .

Using a calculator, we can find that arcsin(0.31)=18 degrees, approximately.

We know that sine of (180-18)=162 degrees is also 0.31. But 162 and 51 degrees add up to more than 180 degrees.

Thus, there is only one triangle that can be formed under these conditions.

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