Question

in triangle qrs, what is the value of tan y°? a $\frac{5}{7}$ b $\frac{7}{5}$ c $\frac{c}{5}$ d $\frac{c}{7}$

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. For angle \(y^{\circ}\) in right - triangle \(QRS\), the side opposite to angle \(y^{\circ}\) is \(QR = 5\) and the side adjacent to angle \(y^{\circ}\) is \(RS=7\).
The formula for the tangent of an angle \(\theta\) in a right - triangle is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Calculate \(\tan y^{\circ}\)

Substitute the lengths of the opposite and adjacent sides into the tangent formula. For \(\theta = y^{\circ}\), we have \(\tan y^{\circ}=\frac{QR}{RS}\).
Since \(QR = 5\) and \(RS = 7\), then \(\tan y^{\circ}=\frac{5}{7}\).

Answer:

A. \(\frac{5}{7}\)