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For an acute angle θ, tan θ = 3/4. What is the value of sin θ?
sin θ = 3/5 (choice A). Tangent is opposite over adjacent, so the legs of the right triangle are 3 and 4; the hypotenuse is √(9 + 16) = 5, and sine is opposite over hypotenuse, 3/5.
We posted this ACT-style trigonometry question on Facebook and Instagram with the line “One sign decides this entire question,” and posted the worked answer on Facebook the next day. The question was written by Brainrise; it is not an official ACT item.
Each wrong choice is a specific slip: 4/5 is cos θ, 3/4 repeats the given tangent, 4/3 flips the tangent, and 5/3 puts the hypotenuse on top. Because θ is acute, sin θ is positive, so the answer is 3/5 and not −3/5.
Why does it matter that the angle is acute?
An acute angle is between 0° and 90°, where sine, cosine and tangent are all positive. Without that condition, sin θ could be −3/5 for an angle in the third quadrant.
Why is 4/5 wrong?
4/5 is adjacent over hypotenuse, which is cos θ. It is a common mix-up of which leg goes on top.
What does it cost to practice ACT questions like this in Brainrise?
The 7-day free trial requires a card; after the trial it is $24 a month for one exam (SAT or ACT) or $36 a month for both, and you can cancel any time. Brainrise is not available to New York residents.
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