Multiple choice

In a right angled triangle $ABC, \angle B = 90^\circ, \tan A = \dfrac{5}{12}$, then:

  1. $\sin A = \dfrac{5}{13}$
  2. $\cot A = \dfrac{5}{13}$
  3. $\sin A = \dfrac{-5}{13}$
  4. $\cos A = \dfrac{13}{5}$
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A Correct answer
Explanation

tan A = 5/12. In a right triangle, opposite=5, adjacent=12. Hypotenuse = sqrt(5^2 + 12^2) = 13. sin A = opposite/hypotenuse = 5/13.

AI explanation

In right triangle ABC with angle B = 90 degrees, tan A is defined as the ratio of the opposite side to the adjacent side, giving us 5/12. This means the side opposite to angle A has a length of 5 units and the adjacent side is 12 units. Using the Pythagorean theorem, the hypotenuse is calculated as sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13. The sine of an angle is the ratio of the opposite side to the hypotenuse, making sin A = 5/13.

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