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
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.

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:
$$\displaystyle\frac{{{\sin{{46}}}^{\circ}}}{{47}}=\frac{{{\sin{{51}}}^{\circ}}}{{x}}$$
$$\displaystyle{x}=\frac{{{47}{\sin{{51}}}^{\circ}}}{{{\sin{{46}}}^{\circ}}}$$
$$\displaystyle{x}\approx{50.8}{c}{m}$$