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Natali [406]
3 years ago
11

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

Mathematics
2 answers:
Ivahew [28]3 years ago
8 0

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

Vitek1552 [10]3 years ago
5 0
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.


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