Question

assigned work 2.6 - sine law part 3
instructions: round trigonometric ratio answers t
round length answers to 1 decimal

1. find the measure of the unknown side or u

a) 23.6 cm

Explanation:

Step1: Find the third - angle

The sum of angles in a triangle is $180^{\circ}$. Let the third angle be $\angle K$. So, $\angle K=180^{\circ}-(75^{\circ}+35^{\circ}) = 70^{\circ}$.

Step2: Apply the sine - law

The sine - law states that $\frac{k}{\sin K}=\frac{l}{\sin L}=\frac{j}{\sin J}$. We know that $k = 23.6$ cm, $\angle K = 70^{\circ}$, $\angle L=35^{\circ}$. We want to find $j$. Using $\frac{j}{\sin J}=\frac{k}{\sin K}$, we have $j=\frac{k\sin J}{\sin K}$.

Step3: Substitute the values

$\sin J=\sin75^{\circ}\approx0.966$, $\sin K=\sin70^{\circ}\approx0.940$, $k = 23.6$ cm. Then $j=\frac{23.6\times0.966}{0.940}\approx24.2$ cm.

Answer:

$j\approx24.2$ cm