HSG.SRT.C.6 math practice. Learn by doing.

HSG.SRT.C.6 practice covers understand that side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Work through 8 free questions with answers and explanations, then continue in the related math games.

Grade 101 mapped skills
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Skills aligned to HSG.SRT.C.6

Right triangle trig from two ratios

Grade 1010 questions
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8 free questions · 0/0 correct

Practice playeasy

In a right triangle, sin⁡α=513\sin\alpha = \dfrac{5}{13} and tan⁡α=512\tan\alpha = \dfrac{5}{12}. What is cos⁡α\cos\alpha?

cos⁡α=sin⁡αtan⁡α=513512=513⋅125=1213\cos\alpha = \dfrac{\sin\alpha}{\tan\alpha} = \dfrac{\dfrac{5}{13}}{\dfrac{5}{12}} = \dfrac{5}{13} \cdot \dfrac{12}{5} = \dfrac{12}{13}, or from the 55-1212-1313 triangle: adjacent 1212, hypotenuse 1313.

Practice playeasy

In a right triangle, sin⁡α=725\sin\alpha = \dfrac{7}{25} and cos⁡α=2425\cos\alpha = \dfrac{24}{25}. What is tan⁡α\tan\alpha?

tan⁡α=sin⁡αcos⁡α=7252425=725⋅2524=724\tan\alpha = \dfrac{\sin\alpha}{\cos\alpha} = \dfrac{\dfrac{7}{25}}{\dfrac{24}{25}} = \dfrac{7}{25} \cdot \dfrac{25}{24} = \dfrac{7}{24}.

Practice playeasy

In a right triangle, sin⁡θ=1213\sin\theta = \dfrac{12}{13} and tan⁡θ=125\tan\theta = \dfrac{12}{5}. What is cos⁡θ\cos\theta?

cos⁡θ=sin⁡θtan⁡θ=1213125=1213⋅512=513\cos\theta = \dfrac{\sin\theta}{\tan\theta} = \dfrac{\dfrac{12}{13}}{\dfrac{12}{5}} = \dfrac{12}{13} \cdot \dfrac{5}{12} = \dfrac{5}{13}.

Practice playeasy

In a right triangle, cos⁡α=513\cos\alpha = \dfrac{5}{13} and tan⁡α=125\tan\alpha = \dfrac{12}{5}. What is sin⁡α\sin\alpha?

sin⁡α=tan⁡α⋅cos⁡α=125⋅513=1213\sin\alpha = \tan\alpha \cdot \cos\alpha = \dfrac{12}{5} \cdot \dfrac{5}{13} = \dfrac{12}{13}.

Practice playeasy

In a right triangle, sin⁡θ=1517\sin\theta = \dfrac{15}{17} and cos⁡θ=817\cos\theta = \dfrac{8}{17}. What is tan⁡θ\tan\theta?

tan⁡θ=sin⁡θcos⁡θ=1517817=1517⋅178=158\tan\theta = \dfrac{\sin\theta}{\cos\theta} = \dfrac{\dfrac{15}{17}}{\dfrac{8}{17}} = \dfrac{15}{17} \cdot \dfrac{17}{8} = \dfrac{15}{8}.

Practice playeasy

In a right triangle, sin⁡α=45\sin\alpha = \dfrac{4}{5} and tan⁡α=43\tan\alpha = \dfrac{4}{3}. What is cos⁡α\cos\alpha?

cos⁡α=sin⁡αtan⁡α=4543=45⋅34=35\cos\alpha = \dfrac{\sin\alpha}{\tan\alpha} = \dfrac{\dfrac{4}{5}}{\dfrac{4}{3}} = \dfrac{4}{5} \cdot \dfrac{3}{4} = \dfrac{3}{5}.

Practice playeasy

In a right triangle, cos⁡θ=1213\cos\theta = \dfrac{12}{13} and tan⁡θ=512\tan\theta = \dfrac{5}{12}. What is sin⁡θ\sin\theta?

sin⁡θ=tan⁡θ⋅cos⁡θ=512⋅1213=513\sin\theta = \tan\theta \cdot \cos\theta = \dfrac{5}{12} \cdot \dfrac{12}{13} = \dfrac{5}{13}.

Practice playeasy

In a right triangle, cos⁡α=2425\cos\alpha = \dfrac{24}{25} and tan⁡α=724\tan\alpha = \dfrac{7}{24}. What is sin⁡α\sin\alpha?

sin⁡α=tan⁡α⋅cos⁡α=724⋅2425=725\sin\alpha = \tan\alpha \cdot \cos\alpha = \dfrac{7}{24} \cdot \dfrac{24}{25} = \dfrac{7}{25}.

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Practice HSG.SRT.C.6 inside a game.

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Tests that assess these skills:
ACTLEAP 2025NY State MathSATSBAC
Test reporting domains
SAT All grades: Geometry and TrigonometryACT All grades: Preparing for Higher MathSBAC High School: Concepts and ProceduresACT Aspire All grades: Preparing for Higher MathATLAS Geometry: Similarity, Right Triangles, and TrigonometryCMAS High school: Geometry
Nearby standards
HSG.GPE.B.6HSG.SRT.C.8All Common Core standards