What you’ll learn
Calculate/use sine.
Key idea
The defining ratio for sin is opposite/hypotenuse.
Sine uses the opposite leg, not either leg; inverse side recovery preserves the ratio order.
Worked example
Enter the exact value or ordered values in the format requested below.
A right triangle has opposite=36, adjacent=15, hypotenuse=39 relative to acute theta. Compute sin(theta) exactly.
- sin(theta)=opposite/hypotenuse=36/39.
- The exact ratio is 12/13; the named side roles determine the order.
Answer: 12/13
Quick Check
Evaluate a worked attempt at calculate/use sine, identify the first invalid step, and provide the correction.
A right triangle has opposite=21, adjacent=20, hypotenuse=29 relative to acute theta. Student Step 1 defines sin(theta)=adjacent/hypotenuse. Step 2 substitutes to get 20/29. Locate the first invalid step and correct the ratio.