Question

Given a right triangle. anglea is 51^circ. A line is drawn from anglec (90^circ) to the hypotenuse, creating a 7^circ angle between the line

Non-right triangles and trigonometry
ANSWERED
asked 2021-09-12
Given a right triangle. anglea is \(\displaystyle{51}^{\circ}\). A line is drawn from anglec \(\displaystyle{\left({90}^{\circ}\right)}\) to the hypotenuse, creating a \(\displaystyle{7}^{\circ}\) angle between the line and the cathetus adjusted to angleb. The cathetus adjusted to angel is 47cm. Find the length of the line drawn.

Expert Answers (1)

2021-09-13
\(\displaystyle\angle{b}={180}^{\circ}-\angle{c}-\angle{a}\)
\(\displaystyle\angle{b}={180}^{\circ}-{90}^{\circ}-{51}^{\circ}\)
\(\displaystyle\angle{b}=={46}^{\circ}\)
Let the line be x. Use the law of Sines:
\(\displaystyle\frac{{{\sin{{46}}}^{\circ}}}{{47}}=\frac{{{\sin{{51}}}^{\circ}}}{{x}}\)
\(\displaystyle{x}=\frac{{{47}{\sin{{51}}}^{\circ}}}{{{\sin{{46}}}^{\circ}}}\)
\(\displaystyle{x}\approx{50.8}{c}{m}\)
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