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
Here are the values from the triangle: Step 1: Find the length of the altitude AD. In the right-angled triangle ABD, we use the Pythagorean theorem: AB^2 = AD^2 + BD^2 22^2 = AD^2 + 11^2 484 = AD^2 + 121 AD^2 = 484 - 121 AD^2 = 363 AD = sqrt(363) = sqrt(121 × 3) = 11sqrt(3) Step 2: Find the length of AC. In the right-angled triangle ACD, we use the Pythagorean theorem: AC^2 = AD^2 + CD^2 AC^2 = (11sqrt(3))^2 + 14^2 AC^2 = 363 + 196 AC^2 = 559 AC = sqrt(559) Now we can find the required trigonometric values: 1. x: In the right-angled triangle ACD: x = AdjacentHypotenuse = CDAC x = (14)/(sqrt(559)) x = (14)/(sqrt(559)) 2. y: In the right-angled triangle ABD: y = OppositeHypotenuse = ADAB y = 11sqrt(3)22 y = sqrt(3)2 3. x: In the right-angled triangle ACD: x = OppositeAdjacent = ADCD x = 11sqrt(3)14 x = 11sqrt(3)14 That's 2 down. 3 left today — send the next one.