If sin A = 3/5, and A is an acute angle, what is the value of tan A?
Correct: A
Given sin A = 3/5. In a right-angled triangle, sin A = Opposite / Hypotenuse. So, let the Opposite side be 3k and the Hypotenuse be 5k for some positive k. Using the Pythagoras theorem, (Adjacent)² + (Opposite)² = (Hypotenuse)². So, (Adjacent)² + (3k)² = (5k)². (Adjacent)² + 9k² = 25k². (Adjacent)² = 25k² - 9k² = 16k². Adjacent = √(16k²) = 4k. Now, tan A = Opposite / Adjacent = 3k / 4k = 3/4.