Question

1. sketch and then solve the following.

a) in △rst, ∠t = 43°, ∠r = 68°, t = 114 cm.

Explanation:

Step1: Find angle S

The sum of angles in a triangle is 180°. So, $\angle S=180^{\circ}-\angle R - \angle T$.
$\angle S = 180^{\circ}-68^{\circ}-43^{\circ}=69^{\circ}$

Step2: Use the sine - law to find side r

The sine - law states that $\frac{r}{\sin R}=\frac{t}{\sin T}$.
$r=\frac{t\sin R}{\sin T}$
Substitute $\angle R = 68^{\circ}$, $\angle T = 43^{\circ}$, and $t = 114$ cm.
$r=\frac{114\times\sin68^{\circ}}{\sin43^{\circ}}$
$\sin68^{\circ}\approx0.9272$, $\sin43^{\circ}\approx0.6820$
$r=\frac{114\times0.9272}{0.6820}\approx154.9$ cm

Step3: Use the sine - law to find side s

The sine - law states that $\frac{s}{\sin S}=\frac{t}{\sin T}$.
$s=\frac{t\sin S}{\sin T}$
Substitute $\angle S = 69^{\circ}$, $\angle T = 43^{\circ}$, and $t = 114$ cm.
$\sin69^{\circ}\approx0.9336$
$s=\frac{114\times0.9336}{0.6820}\approx156.7$ cm

Answer:

$\angle S = 69^{\circ}$, $r\approx154.9$ cm, $s\approx156.7$ cm