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: Find the length of AC using the Pythagorean theorem in ABC. Given AB = 3 cm and BC = 4 cm, and ABC = 90^. AC^2 = AB^2 + BC^2 AC^2 = (3\, cm)^2 + (4\, cm)^2 AC^2 = 9\, cm^2 + 16\, cm^2 AC^2 = 25\, cm^2 AC = sqrt(25\, cm)^2 AC = 5\, cm Step 2: Find the length of CD using the Pythagorean theorem in ACD. Given AD = 13 cm and AC = 5 cm (from Step 1), and ACD = 90^. AD^2 = AC^2 + CD^2 (13\, cm)^2 = (5\, cm)^2 + CD^2 169\, cm^2 = 25\, cm^2 + CD^2 CD^2 = 169\, cm^2 - 25\, cm^2 CD^2 = 144\, cm^2 CD = sqrt(144\, cm)^2 CD = 12\, cm Step 3: Calculate the value of ( DAC). In the right-angled triangle ACD, for angle DAC: The opposite side is CD = 12 cm. The adjacent side is AC = 5 cm. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. ( DAC) = OppositeAdjacent = (CD)/(AC) ( DAC) = 12\, cm5\, cm ( DAC) = (12)/(5) The value of ( DAC) is (12)/(5). Send me the next one 📸