SOHCAHTOA — Sine in a Right Triangle
Question
Answer choices
- 15.811388300842/5
- 5/15.811388300842
- 15/5
- 5/15
- 15/15.811388300842
B Correct answer: B) 5/15.811388300842
Set up the problem carefully before computing. sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
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
SOHCAHTOA: sin = opposite/hypotenuse. Here, opposite = 5 and hypotenuse = 15.811388300842, so sin(θ) = 5/15.811388300842.
Why each wrong answer is wrong
- A) 15.811388300842/5: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- C) 15/5: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- D) 5/15: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- E) 15/15.811388300842: A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
SOHCAHTOA: Sin = Opp/Hyp, Cos = Adj/Hyp, Tan = Opp/Adj. Burn it into memory — every trig question on the ACT begins here.
More Hard Trigonometry
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- Pythagorean IdentityWhat is the value of sin²(θ) + cos²(θ) for any angle θ?
- Tangent in a Right TriangleIn a right triangle, the side opposite angle θ has length 3 and the side adjacent to θ has
- Sine of a Special AngleWhat is sin(60°)?
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