Algebra 1 right triangle trigonometry worksheet

The ratios come from whole-number sides, so they come out exact, and so do the missing sides from a special angle. The calculator questions, a side from any angle or an angle from two sides, round to the tenth or the degree.

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Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Right Triangle Trigonometry Date Period Answer each question. A right triangle has legs $15$ and $8$ and hypotenuse $17$ . Find $\sin A$ , where $A$ is opposite the side of length $15$ A right triangle has legs $120$ and $126$ and hypotenuse $174$ . Find $\cos A$ , where $A$ is opposite the side of length $120$ A right triangle has legs $32$ and $60$ and hypotenuse $68$ . Find $\tan A$ , where $A$ is opposite the side of length $32$ A right triangle has hypotenuse $32$ and an angle of $6 0^{\circ}$ . Find the side $opposite$ it A right triangle has legs $9$ and $12$ and hypotenuse $15$ . Find $\sin A$ , where $A$ is opposite the side of length $9$ A right triangle has legs $9$ and $12$ and hypotenuse $15$ . Find $\cos A$ , where $A$ is opposite the side of length $9$ A right triangle has legs $20$ and $48$ and hypotenuse $52$ . Find $\tan A$ , where $A$ is opposite the side of length $20$ A right triangle has hypotenuse $22$ and an angle of $3 0^{\circ}$ . Find the side $opposite$ it A right triangle has legs $32$ and $60$ and hypotenuse $68$ . Find $\sin A$ , where $A$ is opposite the side of length $32$ A right triangle has legs $48$ and $20$ and hypotenuse $52$ . Find $\cos A$ , where $A$ is opposite the side of length $48$ A right triangle has legs $24$ and $7$ and hypotenuse $25$ . Find $\tan A$ , where $A$ is opposite the side of length $24$ A right triangle has hypotenuse $40$ and an angle of $4 5^{\circ}$ . Find the side $adjacent to$ it A right triangle has legs $12$ and $16$ and hypotenuse $20$ . Find $\sin A$ , where $A$ is opposite the side of length $12$ A right triangle has legs $15$ and $36$ and hypotenuse $39$ . Find $\cos A$ , where $A$ is opposite the side of length $15$ A right triangle has legs $16$ and $12$ and hypotenuse $20$ . Find $\tan A$ , where $A$ is opposite the side of length $16$ A right triangle has hypotenuse $28$ and an angle of $3 0^{\circ}$ . Find the side $opposite$ it A right triangle has legs $40$ and $75$ and hypotenuse $85$ . Find $\sin A$ , where $A$ is opposite the side of length $40$ A right triangle has legs $100$ and $105$ and hypotenuse $145$ . Find $\cos A$ , where $A$ is opposite the side of length $100$ A right triangle has legs $48$ and $20$ and hypotenuse $52$ . Find $\tan A$ , where $A$ is opposite the side of length $48$ A right triangle has hypotenuse $38$ and an angle of $6 0^{\circ}$ . Find the side $adjacent to$ it Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Right Triangle Trigonometry

Date Period

Answer each question.

A right triangle has legs $15$ and $8$ and hypotenuse $17$ . Find $\sin A$ , where $A$ is opposite the side of length $15$
A right triangle has legs $120$ and $126$ and hypotenuse $174$ . Find $\cos A$ , where $A$ is opposite the side of length $120$
A right triangle has legs $32$ and $60$ and hypotenuse $68$ . Find $\tan A$ , where $A$ is opposite the side of length $32$
A right triangle has hypotenuse $32$ and an angle of $6 0^{\circ}$ . Find the side $opposite$ it
A right triangle has legs $9$ and $12$ and hypotenuse $15$ . Find $\sin A$ , where $A$ is opposite the side of length $9$
A right triangle has legs $9$ and $12$ and hypotenuse $15$ . Find $\cos A$ , where $A$ is opposite the side of length $9$
A right triangle has legs $20$ and $48$ and hypotenuse $52$ . Find $\tan A$ , where $A$ is opposite the side of length $20$
A right triangle has hypotenuse $22$ and an angle of $3 0^{\circ}$ . Find the side $opposite$ it
A right triangle has legs $32$ and $60$ and hypotenuse $68$ . Find $\sin A$ , where $A$ is opposite the side of length $32$
A right triangle has legs $48$ and $20$ and hypotenuse $52$ . Find $\cos A$ , where $A$ is opposite the side of length $48$
A right triangle has legs $24$ and $7$ and hypotenuse $25$ . Find $\tan A$ , where $A$ is opposite the side of length $24$
A right triangle has hypotenuse $40$ and an angle of $4 5^{\circ}$ . Find the side $adjacent to$ it
A right triangle has legs $12$ and $16$ and hypotenuse $20$ . Find $\sin A$ , where $A$ is opposite the side of length $12$
A right triangle has legs $15$ and $36$ and hypotenuse $39$ . Find $\cos A$ , where $A$ is opposite the side of length $15$
A right triangle has legs $16$ and $12$ and hypotenuse $20$ . Find $\tan A$ , where $A$ is opposite the side of length $16$
A right triangle has hypotenuse $28$ and an angle of $3 0^{\circ}$ . Find the side $opposite$ it
A right triangle has legs $40$ and $75$ and hypotenuse $85$ . Find $\sin A$ , where $A$ is opposite the side of length $40$
A right triangle has legs $100$ and $105$ and hypotenuse $145$ . Find $\cos A$ , where $A$ is opposite the side of length $100$
A right triangle has legs $48$ and $20$ and hypotenuse $52$ . Find $\tan A$ , where $A$ is opposite the side of length $48$
A right triangle has hypotenuse $38$ and an angle of $6 0^{\circ}$ . Find the side $adjacent to$ it



Sigma Prep · sigmaprep.io/worksheets Name Right Triangle TrigonometryAnswer keyVersion 1 Date Period Answer each question. A right triangle has legs $15$ and $8$ and hypotenuse $17$ . Find $\sin A$ , where $A$ is opposite the side of length $15$ $\frac{15}{17}$ A right triangle has legs $120$ and $126$ and hypotenuse $174$ . Find $\cos A$ , where $A$ is opposite the side of length $120$ $\frac{21}{29}$ A right triangle has legs $32$ and $60$ and hypotenuse $68$ . Find $\tan A$ , where $A$ is opposite the side of length $32$ $\frac{8}{15}$ A right triangle has hypotenuse $32$ and an angle of $6 0^{\circ}$ . Find the side $opposite$ it $16 \sqrt{3}$ A right triangle has legs $9$ and $12$ and hypotenuse $15$ . Find $\sin A$ , where $A$ is opposite the side of length $9$ $\frac{3}{5}$ A right triangle has legs $9$ and $12$ and hypotenuse $15$ . Find $\cos A$ , where $A$ is opposite the side of length $9$ $\frac{4}{5}$ A right triangle has legs $20$ and $48$ and hypotenuse $52$ . Find $\tan A$ , where $A$ is opposite the side of length $20$ $\frac{5}{12}$ A right triangle has hypotenuse $22$ and an angle of $3 0^{\circ}$ . Find the side $opposite$ it $11$ A right triangle has legs $32$ and $60$ and hypotenuse $68$ . Find $\sin A$ , where $A$ is opposite the side of length $32$ $\frac{8}{17}$ A right triangle has legs $48$ and $20$ and hypotenuse $52$ . Find $\cos A$ , where $A$ is opposite the side of length $48$ $\frac{5}{13}$ A right triangle has legs $24$ and $7$ and hypotenuse $25$ . Find $\tan A$ , where $A$ is opposite the side of length $24$ $\frac{24}{7}$ A right triangle has hypotenuse $40$ and an angle of $4 5^{\circ}$ . Find the side $adjacent to$ it $20 \sqrt{2}$ A right triangle has legs $12$ and $16$ and hypotenuse $20$ . Find $\sin A$ , where $A$ is opposite the side of length $12$ $\frac{3}{5}$ A right triangle has legs $15$ and $36$ and hypotenuse $39$ . Find $\cos A$ , where $A$ is opposite the side of length $15$ $\frac{12}{13}$ A right triangle has legs $16$ and $12$ and hypotenuse $20$ . Find $\tan A$ , where $A$ is opposite the side of length $16$ $\frac{4}{3}$ A right triangle has hypotenuse $28$ and an angle of $3 0^{\circ}$ . Find the side $opposite$ it $14$ A right triangle has legs $40$ and $75$ and hypotenuse $85$ . Find $\sin A$ , where $A$ is opposite the side of length $40$ $\frac{8}{17}$ A right triangle has legs $100$ and $105$ and hypotenuse $145$ . Find $\cos A$ , where $A$ is opposite the side of length $100$ $\frac{21}{29}$ A right triangle has legs $48$ and $20$ and hypotenuse $52$ . Find $\tan A$ , where $A$ is opposite the side of length $48$ $\frac{12}{5}$ A right triangle has hypotenuse $38$ and an angle of $6 0^{\circ}$ . Find the side $adjacent to$ it $19$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Right Triangle TrigonometryAnswer keyVersion 1

Date Period

Answer each question.

A right triangle has legs $15$ and $8$ and hypotenuse $17$ . Find $\sin A$ , where $A$ is opposite the side of length $15$ $\frac{15}{17}$
A right triangle has legs $120$ and $126$ and hypotenuse $174$ . Find $\cos A$ , where $A$ is opposite the side of length $120$ $\frac{21}{29}$
A right triangle has legs $32$ and $60$ and hypotenuse $68$ . Find $\tan A$ , where $A$ is opposite the side of length $32$ $\frac{8}{15}$
A right triangle has hypotenuse $32$ and an angle of $6 0^{\circ}$ . Find the side $opposite$ it $16 \sqrt{3}$
A right triangle has legs $9$ and $12$ and hypotenuse $15$ . Find $\sin A$ , where $A$ is opposite the side of length $9$ $\frac{3}{5}$
A right triangle has legs $9$ and $12$ and hypotenuse $15$ . Find $\cos A$ , where $A$ is opposite the side of length $9$ $\frac{4}{5}$
A right triangle has legs $20$ and $48$ and hypotenuse $52$ . Find $\tan A$ , where $A$ is opposite the side of length $20$ $\frac{5}{12}$
A right triangle has hypotenuse $22$ and an angle of $3 0^{\circ}$ . Find the side $opposite$ it $11$
A right triangle has legs $32$ and $60$ and hypotenuse $68$ . Find $\sin A$ , where $A$ is opposite the side of length $32$ $\frac{8}{17}$
A right triangle has legs $48$ and $20$ and hypotenuse $52$ . Find $\cos A$ , where $A$ is opposite the side of length $48$ $\frac{5}{13}$
A right triangle has legs $24$ and $7$ and hypotenuse $25$ . Find $\tan A$ , where $A$ is opposite the side of length $24$ $\frac{24}{7}$
A right triangle has hypotenuse $40$ and an angle of $4 5^{\circ}$ . Find the side $adjacent to$ it $20 \sqrt{2}$
A right triangle has legs $12$ and $16$ and hypotenuse $20$ . Find $\sin A$ , where $A$ is opposite the side of length $12$ $\frac{3}{5}$
A right triangle has legs $15$ and $36$ and hypotenuse $39$ . Find $\cos A$ , where $A$ is opposite the side of length $15$ $\frac{12}{13}$
A right triangle has legs $16$ and $12$ and hypotenuse $20$ . Find $\tan A$ , where $A$ is opposite the side of length $16$ $\frac{4}{3}$
A right triangle has hypotenuse $28$ and an angle of $3 0^{\circ}$ . Find the side $opposite$ it $14$
A right triangle has legs $40$ and $75$ and hypotenuse $85$ . Find $\sin A$ , where $A$ is opposite the side of length $40$ $\frac{8}{17}$
A right triangle has legs $100$ and $105$ and hypotenuse $145$ . Find $\cos A$ , where $A$ is opposite the side of length $100$ $\frac{21}{29}$
A right triangle has legs $48$ and $20$ and hypotenuse $52$ . Find $\tan A$ , where $A$ is opposite the side of length $48$ $\frac{12}{5}$
A right triangle has hypotenuse $38$ and an angle of $6 0^{\circ}$ . Find the side $adjacent to$ it $19$

How to do these

A right triangle has legs $3$ and $4$ and hypotenuse $5$ . Find $\sin A$ , where $A$ is opposite the side of length $3$

Sine is opposite over hypotenuse.
The side opposite A is 3, and the hypotenuse is 5.

The answer is $\frac{3}{5}$ .

Where students go wrong

Using the hypotenuse as the adjacent side. The hypotenuse is never the adjacent one: adjacent means the leg next to the angle, and the hypotenuse has its own name for a reason.

Also called SOHCAHTOA, trig ratios or finding missing sides.

What you can put on this worksheet

Sine from the three sides: A right triangle has legs $45$ and $24$ and hypotenuse $51$ . Find $\sin A$ , where $A$ is opposite the side of length $45$ → $\frac{15}{17}$
Cosine from the three sides: A right triangle has legs $45$ and $24$ and hypotenuse $51$ . Find $\cos A$ , where $A$ is opposite the side of length $45$ → $\frac{8}{17}$
Tangent from the three sides: A right triangle has legs $45$ and $24$ and hypotenuse $51$ . Find $\tan A$ , where $A$ is opposite the side of length $45$ → $\frac{15}{8}$
A missing side from a special angle: A right triangle has hypotenuse $12$ and an angle of $4 5^{\circ}$ . Find the side $adjacent to$ it → $6 \sqrt{2}$
Cosecant, secant and cotangent from the sides: A right triangle has legs $45$ and $24$ and hypotenuse $51$ . Find $\csc A$ , where $A$ is opposite the side of length $45$ → $\frac{17}{15}$
A missing side, any angle, rounded: Find $x$ . Round to the nearest tenth. → $13.9$
An angle from two sides, with inverse trig: Find $θ$ . Round to the nearest degree. → $3 3^{\circ}$

Questions about these worksheets

Yes. Every right triangle trigonometry sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the right triangle trigonometry questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 7: sine from the three sides, cosine from the three sides, tangent from the three sides, a missing side from a special angle, cosecant, secant and cotangent from the sides, a missing side, any angle, rounded and an angle from two sides, with inverse trig. Tick as many as you want and set how many of each, or let it spread them evenly.

Using the hypotenuse as the adjacent side. The hypotenuse is never the adjacent one: adjacent means the leg next to the angle, and the hypotenuse has its own name for a reason.

Algebra 1 right triangle trigonometry worksheet

Select your difficulty

Right Triangle Trigonometry

Right Triangle TrigonometryAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these right triangle trigonometry worksheets free?+

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Is this a free alternative to Kuta Software for right triangle trigonometry?+

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