Question

1. solve the right - angle triangle, rmh, if: r = 18.2m; h = 54.6m; h = 90.0° 3 marks

Explanation:

Step1: Find side m using the Pythagorean theorem

$$m=\sqrt{h^{2}-r^{2}}=\sqrt{54.6^{2}-18.2^{2}}=\sqrt{(54.6 + 18.2)(54.6-18.2)}=\sqrt{72.8\times36.4}=\sqrt{2649.92}\approx51.48m$$

Step2: Find angle R using the sine - function

$$\sin R=\frac{r}{h}=\frac{18.2}{54.6}\approx0.3333$$
$$R=\sin^{- 1}(0.3333)\approx19.47^{\circ}$$

Step3: Find angle M

Since the sum of angles in a triangle is $180^{\circ}$ and $H = 90^{\circ}$, $R\approx19.47^{\circ}$
$$M=180^{\circ}-90^{\circ}-19.47^{\circ}=70.53^{\circ}$$

Answer:

$m\approx51.48m$, $R\approx19.47^{\circ}$, $M\approx70.53^{\circ}$