Similar right triangle trigonometry 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 10 similar right triangle trigonometry problems our math games drill.
CCSS HSG.SRT.C.610 questions in the bank
Sample questions
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Question 1easy
In right triangle ABC, ∠C is the right angle. The three sides measure AB=61, BC=60, and CA=11. Triangle ABC is similar to triangle XYZ, where B corresponds to Y and C corresponds to Z. What is sinY?
Because B corresponds to Y, sinY=sinB. In right triangle ABC, sinB=hypotenuseopposite=ABCA=6111.
Question 2easy
In right triangle ABC, ∠C is the right angle. The three sides measure AB=37, BC=35, and CA=12. Triangle ABC is similar to triangle XYZ, where B corresponds to Y and C corresponds to Z. What is cosY?
Because B corresponds to Y, cosY=cosB. In right triangle ABC, cosB=hypotenuseadjacent=ABBC=3735.
Question 3medium
In right triangle ABC, ∠C is the right angle. The three sides measure AB=25, BC=24, and CA=7. Triangle ABC is similar to triangle DEF, where A corresponds to D and C corresponds to F. What is tanD?
Because A corresponds to D, tanD=tanA. In right triangle ABC, tanA=adjacentopposite=CABC=724.
Question 4medium
In right triangle ABC, ∠A is the right angle. The three sides measure BC=15, CA=12, and AB=9. Triangle ABC is similar to triangle XYZ, where B corresponds to Y and A corresponds to X. What is sinY?
Because B corresponds to Y, sinY=sinB. With the right angle at A, sinB=hypotenuseopposite=BCCA=1512=54.
Question 5medium
In right triangle ABC, ∠C is the right angle. The three sides measure AB=29, BC=21, and CA=20. Triangle ABC is similar to triangle XYZ, where A corresponds to X and C corresponds to Z. What is cosX?
Because A corresponds to X, cosX=cosA. In right triangle ABC, cosA=hypotenuseadjacent=ABCA=2920.
Question 6medium
In right triangle ABC, ∠C is the right angle. The three sides measure AB=41, BC=40, and CA=9. Triangle ABC is similar to triangle DEF, where B corresponds to E and C corresponds to F. What is tanE?
Because B corresponds to E, tanE=tanB. In right triangle ABC, tanB=adjacentopposite=BCCA=409.
Question 7medium
In right triangle ABC, ∠B is the right angle. The three sides measure AC=13, BC=12, and AB=5. Triangle ABC is similar to triangle XYZ, where A corresponds to X and B corresponds to Y. What is sinX?
Because A corresponds to X, sinX=sinA. With the right angle at B, sinA=hypotenuseopposite=ACBC=1312.
Question 8medium
In right triangle ABC, ∠A is the right angle. The three sides measure BC=17, CA=15, and AB=8. Triangle ABC is similar to triangle DEF, where C corresponds to F and A corresponds to D. What is tanF?
Because C corresponds to F, tanF=tanC. With the right angle at A, tanC=adjacentopposite=CAAB=158.
Tests that cover similar right triangle trigonometry: