Question

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

Answer 1

The answer is one. and apparently i need more word soooo, words words words.

Answer 2

From the law of sines, we have:

$\displaystyle{ \frac{\sin \angle X}{x}= \frac{\sin \angle Y}{y}$, 

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


Substituting the known values, we have:



$\displaystyle{ \frac{51^{\circ}}{5}= \frac{\sin \angle Y}{2}$, thus

                           $\displaystyle{ \sin \angle Y=\frac{\sin 51^{\circ}}{5}\cdot2\approx \frac{0.777}{5}\cdot2=0.31$.


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.