Right-triangle trigonometryFind a side with trigonometry
Name: Date:
Find the side marked x, to one decimal place. Use a calculator.
1 cm
2 cm
3 cm
4 cm
5 cm
6 cm
- Free
- Grade 9
- SOHCAHTOA, calculator, rounded
Finding a missing side worksheets
With a right triangle, one angle and one side are enough to find any other side — through sine, cosine or tangent. These free printable worksheets give an angle and a side and ask for the one marked x.
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- Answer key included
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Ready to printFinding a missing side
The answer key prints on a separate page.
What's on this sheet
The whole skill is picking the ratio, and the two sides in play decide it. Opposite and hypotenuse is sine, adjacent and hypotenuse is cosine, opposite and adjacent is tangent — SOHCAHTOA. Once the ratio is set, the missing side comes out by one multiplication or one division. Every figure is drawn to its true shape, so a 35° angle looks like 35° and a student can estimate the length 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 35° is not on the page, it comes from a calculator or a table, and the answer is an irrational number rounded off. Each side is asked to one decimal place, 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° = 18 ÷ x
x=23.5
- The angle is 40°. You know the adjacent (18) 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° = 18 ÷ x.
- Rearrange for x and work it out on a calculator: x = 18 ÷ cos 40° = 23.5.