Solve cos 30 * sin(-50) / tan 70

Question
Solve \(\displaystyle{\cos{{30}}}\cdot\frac{{\sin{{\left(-{50}\right)}}}}{{\tan{{70}}}}\)

Answers (1)

2020-12-25
\(\displaystyle{\sin{{\left(-{50}\right)}}}=-{\sin{{\left({50}\right)}}}\)
so the expression becomes \(\displaystyle-{\cos{{\left({30}\right)}}}\frac{{\sin{{\left({50}\right)}}}}{{\tan{{\left({70}\right)}}}}=-{\sin{{\left({50}\right)}}}\frac{\sqrt{{3}}}{{2}}{\tan{{\left({70}\right)}}}=-{0.2415}\) approx.
\(\displaystyle{\left[{\cos{{\left({30}\right)}}}=\frac{\sqrt{{3}}}{{2}}={0.8660}\right.}\) approx because in right-angled triangle ABC where B=90, C=30, A=60, the sides are in the ratioZSK1, sqrt3, 2ZSK by Pythagoras),
tan(70)=2.7475 approx, sin(50)=0.7660 approx.]ZSK
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