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3 votes
Determine the measure of

1 Answer

3 votes

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} (-88)/(-312)=\cos \angle Q \\ (11)/(39)=\cos \angle Q \end{gathered}

Now we will find the value of the angle Q


m\angle Q=\cos ^(-1)(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

User Snorlax
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