Question

in $\triangle opq$, the measure of $\angle q = 90^\circ$, $qp = 11$, $oq = 60$, and $po = 61$. what ratio represents the tangent of $\angle o$? answer

Explanation:

Step1: Recall the tangent ratio in a right triangle

In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. For $\angle O$ in right triangle $\triangle OPQ$ with $\angle Q = 90^{\circ}$, we need to identify the opposite and adjacent sides relative to $\angle O$.

Step2: Identify the sides relative to $\angle O$

• The side opposite to $\angle O$ is $QP$ (since it does not form $\angle O$ and is opposite to it), and $QP = 11$.
• The side adjacent to $\angle O$ is $OQ$ (since it forms $\angle O$ along with the hypotenuse $PO$), and $OQ=60$.

Step3: Calculate the tangent of $\angle O$

Using the definition of tangent, $\tan(\angle O)=\frac{\text{opposite}}{\text{adjacent}}=\frac{QP}{OQ}$. Substituting the values of $QP = 11$ and $OQ = 60$, we get $\tan(\angle O)=\frac{11}{60}$.

Answer:

$\frac{11}{60}$