Math · Trigonometry
Tangent in a Right Triangle
Medium
Math
Trigonometry
Question
In a right triangle, the side opposite angle θ has length 3 and the side adjacent to θ has length 8. What is tan(θ)?
Answer choices
- 3/8
- 3/8.5440037453175
- 8/3
- 1
- 0
A Correct answer: A) 3/8
Set up the problem carefully before computing. tan = opp/adj — no hypotenuse needed. The hypotenuse is only for sine and cosine.
Carry the arithmetic through one step at a time, double-checking signs and units. The ACT writes wrong answers to catch the most common slips, so an answer that "looks right" without verification is risky.
Plug the answer back into the original expression as a sanity check whenever the problem allows. If the substitution does not balance, you have made an arithmetic mistake earlier in the work.
The underlying rule
tan(θ) = opposite/adjacent = 3/8.
Why each wrong answer is wrong
- B) 3/8.5440037453175: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- C) 8/3: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- D) 1: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- E) 0: A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
tan(θ) = opposite over adjacent. The hypotenuse is irrelevant for tangent. Mixing this up is the #1 trig error.
More Medium Trigonometry
- Sine of a Special AngleWhat is sin(45°)?
- SOHCAHTOA — Sine in a Right TriangleIn a right triangle, the side opposite angle θ has length 8 and the hypotenuse has length
- Pythagorean IdentityWhat is the value of sin²(θ) + cos²(θ) for any angle θ?
- Sine of a Special AngleWhat is sin(60°)?
- SOHCAHTOA — Sine in a Right TriangleIn a right triangle, the side opposite angle θ has length 3 and the hypotenuse has length