CoormaBak9

2021-09-12

Given a right triangle. anglea is ${51}^{\circ }$. A line is drawn from anglec $\left({90}^{\circ }\right)$ to the hypotenuse, creating a ${7}^{\circ }$ angle between the line and the cathetus adjusted to angleb. The cathetus adjusted to angel is 47cm. Find the length of the line drawn.

Benedict

$\mathrm{\angle }b={180}^{\circ }-\mathrm{\angle }c-\mathrm{\angle }a$
$\mathrm{\angle }b={180}^{\circ }-{90}^{\circ }-{51}^{\circ }$
$\mathrm{\angle }b=={46}^{\circ }$
Let the line be x. Use the law of Sines:
$\frac{{\mathrm{sin}46}^{\circ }}{47}=\frac{{\mathrm{sin}51}^{\circ }}{x}$
$x=\frac{47{\mathrm{sin}51}^{\circ }}{{\mathrm{sin}46}^{\circ }}$
$x\approx 50.8cm$

Do you have a similar question?