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's how to solve the problem, assuming ADC is an isosceles right-angled triangle. This assumption is made because the length of DC is not provided, and this is a common way for such problems to be solvable with specific numerical values for the angles. Assumption: ADC is an isosceles right-angled triangle, meaning ADC = DAC = 45^, which implies DC = AC. Step 1: Determine the length of DC. Given AC = 18 and assuming ADC is an isosceles right-angled triangle, then DC = AC. DC = 18 Step 2: Calculate the length of BC. The length of the base BC is the sum of BD and DC. BC = BD + DC BC = 14 + 18 BC = 32 Step 3: Calculate angle x in ABC. ABC is a right-angled triangle at C. We use the tangent function, which is the ratio of the opposite side to the adjacent side. x = oppositeadjacent = (AC)/(BC) x = (18)/(32) x = (9)/(16) To find x, take the inverse tangent: x = ((9)/(16)) x ≈ 29.4^ Step 4: Calculate angle y in ADC. ADC is a right-angled triangle at C. We use the tangent function. y = oppositeadjacent = (AC)/(DC) y = (18)/(18) y = 1 To find y, take the inverse tangent: y = (1) y = 45^ The values of the angles are: x ≈ 29.4^ y = 45^ That's 2 down. 3 left today — send the next one.