This printable worksheet helps students master the basics of trigonometry by calculating sine, cosine, and tangent values for various right-angled triangles using side lengths.

I'll solve the trigonometric ratios for each of the six triangles shown in the image. Let me work through them one by one.

Triangle 1:

This is a right triangle with sides 3, 4, and 5 (hypotenuse).
- sin A = opposite/hypotenuse = 3/5
- cos A = adjacent/hypotenuse = 4/5
- tan A = opposite/adjacent = 3/4

Triangle 2:

This is a right triangle with sides 8, 15, and 17 (hypotenuse).
- sin F = opposite/hypotenuse = 8/17
- cos F = adjacent/hypotenuse = 15/17
- tan F = opposite/adjacent = 8/15

Triangle 3:

This is a right triangle with sides 5, 12, and 13 (hypotenuse).
- sin H = opposite/hypotenuse = 5/13
- cos H = adjacent/hypotenuse = 12/13
- tan H = opposite/adjacent = 5/12

Triangle 4:

This is a right triangle with sides 6, 8, and 10 (hypotenuse).
- sin M = opposite/hypotenuse = 6/10 = 3/5
- cos M = adjacent/hypotenuse = 8/10 = 4/5
- tan M = opposite/adjacent = 6/8 = 3/4

Triangle 5:

This is a right triangle with sides 9, 12, and 15 (hypotenuse).
- sin P = opposite/hypotenuse = 9/15 = 3/5
- cos P = adjacent/hypotenuse = 12/15 = 4/5
- tan P = opposite/adjacent = 9/12 = 3/4

Triangle 6:

This is a right triangle with sides 14, 48, and 50 (hypotenuse).
- sin S = opposite/hypotenuse = 14/50 = 7/25
- cos S = adjacent/hypotenuse = 48/50 = 24/25
- tan S = opposite/adjacent = 14/48 = 7/24

The solutions are based on the standard trigonometric definitions:
- sine = opposite side / hypotenuse
- cosine = adjacent side / hypotenuse
- tangent = opposite side / adjacent side

All answers are given as fractions in simplest form as requested in the instructions.