The value of the variable a is 19.66 and the value of the valriable b is 20.21.
What is the law of sines?
For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by the law of sines,
[tex]\rm \dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
Remember that we took
The sine angle is the length of the side opposite to that angle.
Then the third angle of the triangle will be
x + 75 + 35 = 180
x = 70
[tex]\rm \dfrac{\sin 75^o}{b} = \dfrac{\sin 35^o}{12} = \dfrac{\sin 70^o}{a}[/tex]
From the first two-term, we have
sin 75 / b = sin 35 / 12
b = 20.21
From the last two-term, we have
sin 70 / a = sin 35 / 12
a = 19.66
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