Using the law of sines, it is found that 1 triangle can be formed with the given conditions.
Suppose we have a triangle in which:
The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
Hence, for this problem, we have that the relation is:
[tex]\frac{\sin{64^\circ}}{10} = \frac{\sin{G}}{9}[/tex]
[tex]\sin{G} = 0.9\sin{64^\circ}[/tex]
[tex]\sin{G} = 0.8089[/tex]
[tex]G = \arcsin{0.8089}[/tex]
G = 54º
A triangle can have one angle of 64º and another of 54º, hence 1 triangle can be formed with the given conditions.
More can be learned about the law of sines at https://brainly.com/question/25535771
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