Geometry and TrigonometryMediumTrigonometric ratios (tangent)
Geometry and Trigonometry practice question
In a right triangle, the side opposite angle θ has length 8 and the side adjacent to angle θ has length 15. What is the value of tan θ? (Give your answer as a fraction.)
Answer: 8/15
tan θ = opposite / adjacent = 8/15 (the 'TOA' in SOH-CAH-TOA). Do not use the hypotenuse (17 here) — tangent is the ratio of the two legs, not a leg over the hypotenuse.
Common wrong answers
- If you answered 15/8
- You flipped the ratio to adjacent/opposite; tangent is opposite over adjacent, so 8/15.
- If you answered 8/17
- That's sin θ — you divided by the hypotenuse 17 instead of the adjacent leg 15.
- If you answered 15/17
- That's cos θ — tangent uses the two legs only: opposite/adjacent = 8/15.
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