This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: In a right-angle triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Given A = (9)/(10). This means: Opposite side = 9 units Hypotenuse = 10 units Step 2: Use the Pythagorean theorem to find the length of the adjacent side. Let the adjacent side be x. (Opposite)^2 + (Adjacent)^2 = (Hypotenuse)^2 9^2 + x^2 = 10^2 81 + x^2 = 100 Step 3: Solve for x. x^2 = 100 - 81 x^2 = 19 x = sqrt(19) So, the adjacent side is sqrt(19) units. Step 4: Now we can find the other trigonometric ratios for angle A. The cosine of angle A is AdjacentHypotenuse. A = sqrt(19)10 The tangent of angle A is OppositeAdjacent. A = (9)/(sqrt(19)) To rationalize the denominator for A: A = (9)/(sqrt(19)) × sqrt(19)sqrt(19) = 9sqrt(19)19 The adjacent side is sqrt(19), A = sqrt(19)10, and A = 9sqrt(19)19. Adjacent side = sqrt(19), A = sqrt(19)10, A = 9sqrt(19)19 Last free one today — make it count tomorrow, or type /upgrade for unlimited.