Final answer:
The statement is true; knowing sin(α) = 4/5 in a right triangle allows you to determine cos(α) and tan(α) using the Pythagorean theorem and trigonometric identities.
Step-by-step explanation:
The statement is True. In a right triangle with an angle α (alpha), if you know sin(α) = 4/5, you can find cos(α) and tan(α) using the Pythagorean theorem and trigonometric identities. Since sin(α) is the ratio of the opposite side to the hypotenuse (4/5 in this case), you can determine that the opposite side (y) is 4 and the hypotenuse (h) is 5. Applying the Pythagorean theorem (x² + y² = h²), we can find the adjacent side (x): x² = h² - y², thus x² = 25 - 16, which gives x = 3. Therefore, cos(α) = x/h = 3/5. The tangent, which is the ratio of the opposite side to the adjacent side (tan(α) = y/x), is tan(α) = 4/3.