Question

In ΔWXY, w = 880 cm, ∠X=33° and ∠Y=38°. Find the length of y, to the nearest centimeter.

Answer 1

Answer:

$y\approx573cm$

Step-by-step explanation:

First, take a look to the picture that I attached,  however please note the triangle is not drawn to scale, the figure is just to provide visual aid. As you can see the value of $\angle W =109^{\circ}$ this is because of the sum of the interior angles in a triangle is always equal to 180°. So:

$\angle W + \angle X + \angle Y =180\\\\\angle W = 180- \angle X -\angle Y\\\\\angle W =180-38-33\\\\\angle W=109$

Now, we can use the law of sines, which states:

$\frac{w}{sin(W)} =\frac{x}{sin(X)} =\frac{y}{sin(Y)}$

Hence:

$\frac{w}{sin(W)} =\frac{y}{sin(Y)}\\\\\frac{880}{sin(109)} =\frac{y}{sin(38)}\\\\Solving\hspace{3}for\hspace{3}y\\\\y=\frac{880*sin(38)}{sin(109)} \\\\y=572.9999518\approx 573 cm$