Question

a right triangle has side lengths d, e, and f as shown below. use these lengths to find sinx, tanx, and cosx.

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\tan x = \frac{\text{opposite}}{\text{adjacent}}\), \(\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}\).
For angle \(x\), the side opposite to \(x\) is \(d\), the side adjacent to \(x\) is \(f\), and the hypotenuse is \(e\).

Step2: Calculate \(\sin x\)

\(\sin x=\frac{d}{e}\)

Step3: Calculate \(\tan x\)

\(\tan x=\frac{d}{f}\)

Step4: Calculate \(\cos x\)

\(\cos x=\frac{f}{e}\)

Answer:

\(\sin x=\frac{d}{e}\), \(\tan x=\frac{d}{f}\), \(\cos x=\frac{f}{e}\)