Write a trigonometric ratioWrite sine, cosine and tangent ratios
Name: Date:
Write each ratio as a fraction. Read the sides straight off the triangle.
1 cos A =
2 sin B =
3 tan B =
4 tan B =
5 sin A =
6 sin A =
7 cos A =
8 cos B =
- Free
- Grade 9
- Pythagorean triples, fractions
Trigonometric ratios worksheets
Before the calculator comes the definition: in a right triangle the sine, cosine and tangent of an angle are just ratios of its sides. These free printable worksheets give a right triangle with whole-number sides and ask for each ratio as a fraction.
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Ready to printTrigonometric ratios
The answer key prints on a separate page.
What's on this sheet
Every triangle here is a Pythagorean triple — 3-4-5, 5-12-13, 8-15-17 and the rest — so all three sides are whole numbers and every ratio reduces to a clean fraction. That is what lets the page skip the calculator: sin A is not a rounded decimal, it is the opposite over the hypotenuse, read straight off the figure and written as it stands.
Why this sheet works
The skill is naming the sides from the angle that is marked. Opposite is the side across from it, adjacent is the side it touches, and the hypotenuse is the slant — SOH-CAH-TOA. The same triangle can be asked for sin, then cos, then tan, so the child has to keep re-reading which two sides each ratio wants rather than settling into one answer.
How this one works
One question from this sheet, worked through a step at a time.
Write cos A as a fraction
cos A=adjacent / hypotenuse
cos A=24/25
cos A=24/25
- cos A is adjacent over hypotenuse. Name the two sides you need, measured from angle A.
- Read them off the triangle: the adjacent side of angle A is 24, the hypotenuse is 25.
- So cos A = 24/25.