Question

1. in △def, ∠d = 34°, ∠f = 77° and side de = 15.3 cm, find the length of ef, to the nearest tenth (2 marks)

Explanation:

Step1: Find angle E

The sum of angles in a triangle is 180°. So, $\angle E=180^{\circ}-\angle D - \angle F$.
$\angle E = 180^{\circ}-34^{\circ}-77^{\circ}=69^{\circ}$

Step2: Use the sine - rule

The sine - rule states that $\frac{EF}{\sin D}=\frac{DE}{\sin F}$.
We know that $DE = 15.3$ cm, $\angle D=34^{\circ}$, and $\angle F = 77^{\circ}$.
So, $EF=\frac{DE\times\sin D}{\sin F}$.
Substitute the values: $EF=\frac{15.3\times\sin34^{\circ}}{\sin77^{\circ}}$.
Since $\sin34^{\circ}\approx0.5592$ and $\sin77^{\circ}\approx0.9744$.
$EF=\frac{15.3\times0.5592}{0.9744}=\frac{8.55576}{0.9744}\approx8.8$ cm.

Answer:

$8.8$ cm