In a right triangle, if the side opposite θ is 3 and the adjacent is 4, what is tan θ?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

In a right triangle, if the side opposite θ is 3 and the adjacent is 4, what is tan θ?

Explanation:
Tangent of an angle in a right triangle is the ratio of the side opposite the angle to the side adjacent to the angle. With the opposite side measuring 3 and the adjacent side measuring 4, tan θ equals 3/4. This makes sense in a 3-4-5 right triangle pattern, since the hypotenuse would be 5, confirming a valid triangle. The other options don’t match the opposite-to-adjacent ratio: 4/3 is the reciprocal of tan θ (cotangent), sqrt(2) would imply a different angle where opposite and adjacent relate by a factor of √2, and 1/2 isn’t the ratio given.

Tangent of an angle in a right triangle is the ratio of the side opposite the angle to the side adjacent to the angle. With the opposite side measuring 3 and the adjacent side measuring 4, tan θ equals 3/4. This makes sense in a 3-4-5 right triangle pattern, since the hypotenuse would be 5, confirming a valid triangle. The other options don’t match the opposite-to-adjacent ratio: 4/3 is the reciprocal of tan θ (cotangent), sqrt(2) would imply a different angle where opposite and adjacent relate by a factor of √2, and 1/2 isn’t the ratio given.

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