Question

1. sin x

triangle with right angle at y, zy=40, xy=30, zx=50
a) \\(\frac{4}{5}\\) b) \\(\frac{5}{4}\\)
c) \\(\frac{3}{5}\\) d) \\(\frac{5}{3}\\)

Explanation:

Step1: Recall the sine function definition

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

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

For angle \(X\), the opposite side to \(X\) is \(YZ = 40\), and the hypotenuse \(XZ=50\).

Step3: Calculate \(\sin X\)

Using the formula \(\sin X=\frac{YZ}{XZ}\), substitute \(YZ = 40\) and \(XZ = 50\). So, \(\sin X=\frac{40}{50}=\frac{4}{5}\).

Answer:

A. $\frac{4}{5}$