What you’ll learn
Calculate/use cosine.
Key idea
The defining ratio for cos is adjacent/hypotenuse.
The adjacent leg excludes the hypotenuse and is relative to the reference acute angle.
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 cos(theta) exactly.
- cos(theta)=adjacent/hypotenuse=15/39.
- The exact ratio is 5/13; the named side roles determine the order.
Answer: 5/13
Quick Check
Evaluate a worked attempt at calculate/use cosine, 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 cos(theta)=opposite/hypotenuse. Step 2 substitutes to get 21/29. Locate the first invalid step and correct the ratio.