Right-triangle trigonometryFind a side or an angle with trigonometry
Name: Date:
Find the value marked x. Use a calculator; round a side to one decimal place and an angle to the nearest degree.
1 cm
2 degrees
3 cm
4 degrees
5 cm
6 degrees
- Free
- Grade 9
- SOHCAHTOA, calculator, rounded
Right-triangle trigonometry worksheets
Once a triangle has a right angle, one more angle or one more side pins down the rest — through sine, cosine and tangent. These free printable worksheets give a right triangle and ask for the side or angle marked x.
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- Answer key included
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Ready to printRight-triangle trigonometry
The answer key prints on a separate page.
What's on this sheet
The whole skill is choosing the ratio, and the choice is made by which two sides are in play. Opposite and hypotenuse is sine, adjacent and hypotenuse is cosine, opposite and adjacent is tangent — SOHCAHTOA. Every figure is drawn to its true shape, so a 30° angle looks like 30° and a child can estimate the answer before reaching for the calculator, then check the estimate against it.
Why this sheet works
This is a calculator worksheet, and that is why it prints rather than being answered on screen: sin 40° is not on the page, it comes from a calculator or a table, and the answer is an irrational rounded off. A side is asked to one decimal place and an angle to the nearest degree, and the answer key gives the rounded value. It is the honest form of the topic — a page a student works with a calculator beside them.
How this one works
One question from this sheet, worked through a step at a time.
Find the hypotenuse, angle 40°
adjacent ÷ hypotenuse=cosine
cos 40° = 13 ÷ x
x=17
- The angle is 40°. You know the adjacent (13) and you want the hypotenuse (x). Those two sides are the adjacent and the hypotenuse, so the ratio is the cosine.
- Write it with the numbers: cos 40° = 13 ÷ x.
- Rearrange for x and work it out on a calculator: x = 13 ÷ cos 40° = 17.