Finding sine, cosine, tangent Worksheets - Free Printable

We are given a right triangle XYZ, with the right angle at Y.

The sides are:
- XY = 32 (adjacent to angle X)
- YZ = 24 (opposite to angle X)
- XZ = 40 (hypotenuse — longest side, opposite the right angle)

We are asked to find sin X.

Recall:
In a right triangle,
> sin(angle) = opposite / hypotenuse

For angle X:
- The side opposite to angle X is YZ = 24
- The hypotenuse is XZ = 40

So:

sin X = 24 / 40

Now simplify the fraction:

Both 24 and 40 can be divided by 8:

24 ÷ 8 = 3
40 ÷ 8 = 5

So, sin X = 3/5

✔ Double-check:
Is 24/40 really equal to 3/5?
Yes: 24 ÷ 8 = 3, 40 ÷ 8 = 5 → correct.

Also, we can check if this makes sense:
In a right triangle, sine should be between 0 and 1. 3/5 = 0.6 → that’s reasonable.

Final Answer:
3/5