Question

quiz 5: uncertainty and right angle trigonometry b 4. solve the right - angle, rmh triangle if: r = 10.8ft; h = 14.6ft; h = 90.0° 6 marks

Explanation:

Step1: Find side m using Pythagorean theorem

By the Pythagorean theorem $m=\sqrt{h^{2}-r^{2}}$. Substitute $r = 10.8$ and $h=14.6$. So $m=\sqrt{14.6^{2}-10.8^{2}}=\sqrt{(14.6 + 10.8)(14.6-10.8)}=\sqrt{25.4\times3.8}=\sqrt{96.52}\approx9.82$ ft.

Step2: Find angle R

We know that $\sin R=\frac{r}{h}$. So $\sin R=\frac{10.8}{14.6}\approx0.7397$. Then $R=\sin^{- 1}(0.7397)\approx48.1^{\circ}$.

Step3: Find angle M

Since the sum of angles in a triangle is $180^{\circ}$ and $H = 90^{\circ}$, $M=180^{\circ}-90^{\circ}-R$. So $M = 180^{\circ}-90^{\circ}-48.1^{\circ}=41.9^{\circ}$.

Answer:

$m\approx9.82$ ft, $R\approx48.1^{\circ}$, $M\approx41.9^{\circ}$