Final answer:
To find the exact value of sin A with given tan A = 7/120 in Quadrant I, we deduce the hypotenuse via the Pythagorean theorem and then divide the opposite side by the hypotenuse to get sin A ≈ 0.05815, in radical form with a rational denominator.
Step-by-step explanation:
To find the exact value of sin A given that tan A = 7/120 and angle A is in Quadrant I, we use the trigonometric identity sin^2 A + cos^2 A = 1. Since tan A is opposite over adjacent, we can consider the opposite side to be 7 and the adjacent side to be 120. By the Pythagorean theorem, the hypotenuse of the right triangle formed is √(7^2 + 120^2)
Then the hypotenuse, h, is √(49 + 14400) = √14449, thus h = 120.373.
Now sin A is the opposite side over the hypotenuse, so sin A = 7/h. Therefore, sin A in its exact value with a rational denominator is 7/120.373. Simplifying this, it gives us the sin A ≈ 0.05815, which is the sine of angle A in simplest radical form with a rational denominator.