Question

solve the triangle.
write each answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

Step1: Find angle at X

The sum of angles in a triangle is $180^\circ$.
$\angle X = 180^\circ - 40^\circ - 118^\circ = 22^\circ$

Step2: Solve for side $x$ (Law of Sines)

Set up ratio for side $x$.
$\frac{x}{\sin(22^\circ)} = \frac{12}{\sin(118^\circ)}$
$x = \frac{12 \times \sin(22^\circ)}{\sin(118^\circ)}$
$x \approx \frac{12 \times 0.3746}{0.8829} \approx 5.1$

Step3: Solve for side $y$ (Law of Sines)

Set up ratio for side $y$.
$\frac{y}{\sin(40^\circ)} = \frac{12}{\sin(118^\circ)}$
$y = \frac{12 \times \sin(40^\circ)}{\sin(118^\circ)}$
$y \approx \frac{12 \times 0.6428}{0.8829} \approx 8.7$

Answer:

$\angle X = 22^\circ$, $x \approx 5.1$, $y \approx 8.7$