Question

Determine the measure of

Answer 1

We will use the cosine rule to find the measure of angle Q

The cosine rule is

$(RS)^2=(QR)^2+(QS)^2-2(QR)(QS)\cos \angle Q$

RS = 15, QR = 13, QS = 12

Substitute them in the rule above

$\begin{gathered} (15)^2=(13)^2+(12)^2-2(13)(12)\cos \angle Q \\ 225=169+144-312\cos \angle Q \\ 225=313-312\cos \angle Q \end{gathered}$

Subtract 313 from both sides

$-88=-312\cos \angle Q$

Divide both sides by - 312

$\begin{gathered} \frac{-88}{-312}=\cos \angle Q \\ \frac{11}{39}=\cos \angle Q \end{gathered}$

Now we will find the value of the angle Q

$m\angle Q=\cos ^{-1}\frac{11}{39}=73.61733$

Round it to the nearest tenth

The measure of angle Q is 73.6 degrees

First answer

You can consider it as 73.5 degrees