Question

1. in the right triangle pqr below, the measure of ∠r is 90°, pq = 4 units, rq = 3 units. what is tan q?

Explanation:

Step1: Recall the definition of tangent in a right - triangle

In a right - triangle, for an acute angle \(A\), \(\tan A=\frac{\text{opposite}}{\text{adjacent}}\). For angle \(Q\) in right - triangle \(PQR\) with \(\angle R = 90^{\circ}\), the side opposite to \(\angle Q\) is \(PR=\sqrt{7}\) and the side adjacent to \(\angle Q\) is \(RQ = 3\).

Step2: Calculate \(\tan Q\)

Using the formula \(\tan Q=\frac{\text{opposite}}{\text{adjacent}}\), we substitute the values. \(\tan Q=\frac{PR}{RQ}\). Since \(PR = \sqrt{7}\) and \(RQ=3\), \(\tan Q=\frac{\sqrt{7}}{3}\).

Answer:

\(\frac{\sqrt{7}}{3}\) (corresponding to the fourth option)