Grade 10 · Geometry & measurement

Trig ratios and unit circle values practice

Trig ratios and unit circle values is a grade 10 math skill aligned to Common Core standard HSG.SRT.C.6: understand that side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 18 trig ratios and unit circle values problems our math games drill.

CCSS HSG.SRT.C.618 questions in the bank
Sample questions

Try 8 for free

Question 1easy

In a right triangle, the side adjacent to angle θ\theta has length 9 and the hypotenuse has length 41. What is cos⁡θ\cos\theta? Give your answer as a fraction in lowest terms.

cos⁡θ=adjacenthypotenuse=941\cos\theta = \dfrac{\text{adjacent}}{\text{hypotenuse}} = \dfrac{9}{41}.

Question 2easy

In a right triangle, the side adjacent to angle θ\theta has length 24 and the hypotenuse has length 25. What is cos⁡θ\cos\theta? Give your answer as a fraction in lowest terms.

cos⁡θ=adjacenthypotenuse=2425=2425\cos\theta = \dfrac{\text{adjacent}}{\text{hypotenuse}} = \dfrac{24}{25} = \dfrac{24}{25}.

Question 3easy

In a right triangle, the side opposite angle θ\theta has length 4 and the hypotenuse has length 5. What is sin⁡θ\sin\theta? Give your answer as a fraction in lowest terms.

sin⁡θ=oppositehypotenuse=45\sin\theta = \dfrac{\text{opposite}}{\text{hypotenuse}} = \dfrac{4}{5}.

Question 4easy

In a right triangle, the side opposite angle θ\theta has length 3 and the hypotenuse has length 5. What is sin⁡θ\sin\theta? Give your answer as a fraction in lowest terms.

sin⁡θ=oppositehypotenuse=35=35\sin\theta = \dfrac{\text{opposite}}{\text{hypotenuse}} = \dfrac{3}{5} = \dfrac{3}{5}.

Question 5easy

In a right triangle, the side opposite angle θ\theta has length 15 and the side adjacent has length 8. What is tan⁡θ\tan\theta? Give your answer as a fraction in lowest terms.

tan⁡θ=oppositeadjacent=158\tan\theta = \dfrac{\text{opposite}}{\text{adjacent}} = \dfrac{15}{8}.

Question 6easy

In a right triangle, the side opposite angle θ\theta has length 5 and the side adjacent has length 12. What is tan⁡θ\tan\theta? Give your answer as a fraction in lowest terms.

tan⁡θ=oppositeadjacent=512=512\tan\theta = \dfrac{\text{opposite}}{\text{adjacent}} = \dfrac{5}{12} = \dfrac{5}{12}.

Question 7easy

What is cos⁡60°\cos 60°?

Standard unit-circle value: cos⁡60°=12\cos 60° = \dfrac{1}{2}.

Question 8easy

In a right triangle, the side adjacent to angle θ\theta has length 21 and the hypotenuse has length 29. What is cos⁡θ\cos\theta? Give your answer as a fraction in lowest terms.

cos⁡θ=adjacenthypotenuse=2129=2129\cos\theta = \dfrac{\text{adjacent}}{\text{hypotenuse}} = \dfrac{21}{29} = \dfrac{21}{29}.

Tests that cover trig ratios and unit circle values:
SBACACTSATLEAP 2025NY State Math
More Grade 10 skills:
Surface area and volumeSurface area in context (SAT)Special right trianglesSimilar right triangle trigonometryPerimeter and arc lengthMidpoint formulaEquation of a circleCircle theoremsAll Grade 10 practice →

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