Question

express \\(\sin t\\) as a fraction in simplest terms.

triangle image with right angle at s, side sr = \\(\sqrt{5}\\), side tr = 23, vertices t, s, r

answer attempt 1 out of 2
\\(\sin t = \\) input box submit answer

Explanation:

Step1: Recall sine definition for right triangles

For an acute angle in a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Identify sides for angle $T$

• Opposite side to $\angle T$: $SR = \sqrt{5}$
• Hypotenuse: $TR = 23$

Step3: Substitute values into sine formula

$\sin T = \frac{\text{Opposite to } T}{\text{Hypotenuse}} = \frac{\sqrt{5}}{23}$

Answer:

$\frac{\sqrt{5}}{23}$