Question

Suppose that m /_BCA=70^@, and x=33 cm and y = 47 cm. What is the degree measure of /_ABC? 01510101651.png

Non-right triangles and trigonometry
ANSWERED
asked 2020-12-27
Suppose that \(\displaystyle{m}\angle{B}{C}{A}={70}^{\circ}\), and x=33 cm and y = 47 cm. What is the degree measure of \(\displaystyle\angle{A}{B}{C}\)?
image

Answers (1)

2020-12-28
\(\displaystyle{A}{B}=\sqrt{{{A}{C}^{{2}}+{B}{C}^{{2}}-{\left({2}\cdot{A}{C}\cdot{B}{C}{\cos}\angle{B}{C}{A}\right)}}}\)
\(\displaystyle{A}{B}=\sqrt{{{47}^{{2}}+{33}^{{2}}-{\left({2}\cdot{47}\cdot{33}{\cos{{70}}}^{\circ}\right)}}}\)
\(\displaystyle{A}{B}=\sqrt{{{2237.05}}}\)
\(\displaystyle{A}{B}={47.29}\)
Using the cosine law,
\(\displaystyle\angle{A}{B}{C}={{\cos}^{{-{{1}}}}{\left(\frac{{{B}{C}^{{2}}+{A}{B}^{{2}}-{A}{C}^{{2}}}}{{{2}\cdot{B}{C}\cdot{A}{B}}}\right)}}\)
\(\displaystyle\angle{A}{B}{C}={{\cos}^{{-{{1}}}}{\left(\frac{{{33}^{{2}}+{47.29}^{{2}}-{47}^{{2}}}}{{{2}\cdot{33}\cdot{47.29}}}\right)}}\)
\(\displaystyle\angle{A}{B}{C}={{\cos}^{{-{{1}}}}{\left({0.3576}\right)}}\)
\(\displaystyle\angle{A}{B}{C}={{\cos}^{{-{{1}}}}=}{69.04}^{\circ}\)
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