Which equation could be used to solve for the measure of side q in triangle QRS shown, given s is equal to 15 , cap s is equal to 45 degrees , and cap q is equal to 105 degrees ?
Answer
A
the fraction with numerator sine 105 degrees and denominator 15 is equal to the fraction with numerator sine 30 degrees and denominator q
B
the fraction with numerator sine 105 degrees and denominator q is equal to the fraction with numerator sine 30 degrees and denominator 15
C
the fraction with numerator 15 and denominator sine 105 degrees is equal to the fraction with numerator q and denominator sine 45 degrees
D
the fraction with numerator q and denominator sine 105 degrees is equal to the fraction with numerator 15 and denominator sine 45 degrees
Explanation
The Law of Sines pairs each side with the sine of its opposite angle. Since side s = 15 is opposite angle S = 45°, and side q is opposite angle Q = 105°, set q/sin(105°) = 15/sin(45°). This is the equation in choice B. The remaining angle is 30°, but it is opposite the third side, not the side of length 15.
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