Question

2 the diagram below shows right triangle upc. which ratio represents the sine of ∠u? 1) \\( \frac { 15 } { 8 } \\) 2) \\( \frac { 15 } { 17 } \\) 3) \\( \frac { 8 } { 15 } \\) 4) \\( \frac { 8 } { 17 } \\)

Explanation:

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

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Identify the sides relative to \(\angle U\)

For \(\angle U\), the side opposite to \(\angle U\) is \(PC = 15\), and the hypotenuse is \(UP=17\).

Step3: Calculate \(\sin\angle U\)

Using the formula \(\sin\angle U=\frac{\text{opposite}}{\text{hypotenuse}}\), we substitute the values: \(\sin\angle U=\frac{PC}{UP}\).

Answer:

1. \(\frac{15}{17}\)