Worked example
In a right triangle, the side opposite θ is 3, the adjacent side is 4, and the hypotenuse is 5. What is sin(θ)? Give an exact fraction.
Answer & why
Answer:
sin(θ) = opposite/hypotenuse = 3/5.
Grade 10 · Math
Use a right-triangle sine ratio
Find an exact sine ratio from labeled right-triangle side lengths.
8 authored questions + worked example
Add to plan
All questions
All 8 authored questions for this skill.
Question 1
In a right triangle, the side opposite θ is 12, the adjacent side is 35, and the hypotenuse is 37. What is sin(θ)? Give an exact fraction.
A hint
Sine uses the opposite side over the hypotenuse.
Answer & why
Answer:
sin(θ) = opposite/hypotenuse = 12/37.
Question 2
In a right triangle, the side opposite θ is 11, the adjacent side is 60, and the hypotenuse is 61. What is sin(θ)? Give an exact fraction.
A hint
Sine uses the opposite side over the hypotenuse.
Answer & why
Answer:
sin(θ) = opposite/hypotenuse = 11/61.
Question 3
In a right triangle, the side opposite θ is 3, the adjacent side is 4, and the hypotenuse is 5. What is sin(θ)? Give an exact fraction.
A hint
Sine uses the opposite side over the hypotenuse.
Answer & why
Answer:
sin(θ) = opposite/hypotenuse = 3/5.
Question 4
In a right triangle, the side opposite θ is 5, the adjacent side is 12, and the hypotenuse is 13. What is sin(θ)? Give an exact fraction.
A hint
Sine uses the opposite side over the hypotenuse.
Answer & why
Answer:
sin(θ) = opposite/hypotenuse = 5/13.
Question 5
In a right triangle, the side opposite θ is 8, the adjacent side is 15, and the hypotenuse is 17. What is sin(θ)? Give an exact fraction.
A hint
Sine uses the opposite side over the hypotenuse.
Answer & why
Answer:
sin(θ) = opposite/hypotenuse = 8/17.
Question 6
In a right triangle, the side opposite θ is 7, the adjacent side is 24, and the hypotenuse is 25. What is sin(θ)? Give an exact fraction.
A hint
Sine uses the opposite side over the hypotenuse.
Answer & why
Answer:
sin(θ) = opposite/hypotenuse = 7/25.
Question 7
In a right triangle, the side opposite θ is 20, the adjacent side is 21, and the hypotenuse is 29. What is sin(θ)? Give an exact fraction.
A hint
Sine uses the opposite side over the hypotenuse.
Answer & why
Answer:
sin(θ) = opposite/hypotenuse = 20/29.
Question 8
In a right triangle, the side opposite θ is 9, the adjacent side is 40, and the hypotenuse is 41. What is sin(θ)? Give an exact fraction.
A hint
Sine uses the opposite side over the hypotenuse.
Answer & why
Answer:
sin(θ) = opposite/hypotenuse = 9/41.