What you’ll learn
Calculate/use tangent.
Key idea
The defining ratio for tan is opposite/adjacent.
Tangent uses both legs and may exceed one; inverting a ratio changes its meaning.
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 tan(theta) exactly.
- tan(theta)=opposite/adjacent=36/15.
- The exact ratio is 12/5; the named side roles determine the order.
Answer: 12/5
Quick Check
Evaluate a worked attempt at calculate/use tangent, 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 tan(theta)=adjacent/opposite. Step 2 substitutes to get 20/21. Locate the first invalid step and correct the ratio.