Final answer:
To find sin A given tan A = √(5) and cos A > 0, we use the Pythagorean identity and the relationship between sin, cos, and tan. After finding cos A, we determine sin A is approximately 2√(5)/5.
Step-by-step explanation:
The question asks us to find sin A given that tan A = √(5) and cos A > 0. To find sin A, we can use the Pythagorean identity in trigonometry, which relates sin, cos, and tan of an angle. The identity is sin² A + cos² A = 1. Since tan A = sin A / cos A, we can express sin A in terms of tan A and cos A as sin A = tan A * cos A. Given tan A = √(5), this becomes sin A = √(5) * cos A.
To find cos A, considering that tan² A + 1 = 1/cos² A, we substitute tan A with √(5) and get cos² A = 1/(5 + 1) = 1/6, so cos A = √(1/6), since cos A is positive as given by the condition. Now we can compute sin A = √(5) * √(1/6) = √(5/6). Simplifying further, sin A = √(5) / √(6) = √(5) * √(6) / 6 = √(30) / 6 = √(5 * 6) / 6 = √(5) / √(6).
Substituting the value of √(6) with its decimal equivalent, which is approximately 2.45, the sin A = √(5) / 2.45, which simplifies to approximately 2√(5)/5.