Question

What is the value of z, rounded to the nearest tenth? use the law of sines to find the answer.

Answer 1

We can change the law of sines a little bit to match our problem.

$\sf\dfrac{sin(X)}{x}=\dfrac{sin(Y)}{y}=\dfrac{sin(Z)}{z}$

We know what angle Y is and what side y is, so let's use that along with angle Z and side z:

$\sf\dfrac{sin(Y)}{y}=\dfrac{sin(Z)}{z}$

Plug in what we know:

$\sf\dfrac{sin(51)}{2.6}=\dfrac{sin(76)}{z}$

Multiply 'z' to both sides:

$\sf\dfrac{sin(51)}{2.6}z=sin(76)$

Divide sin(51)/2.6 to both sides:

$\sf z=\dfrac{sin(76)(2.6)}{sin(51)}$

Plug it into your calculator.

$\boxed{\sf z\approx 3.2}$

Answer 2

Your answer is

3.2 units