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: Establish the positions of points X, Y, and Z relative to each other. Let point X be the origin (0,0). Point Y is 15 km south of X. This means Y is at coordinates (0, -15). Point Z is 20 km from X on a bearing of 270^. A bearing of 270^ is due west. This means Z is at coordinates (-20, 0). Step 2: Recognize the geometric shape formed by points X, Y, and Z. Since Y is directly south of X and Z is directly west of X, the lines XY and XZ are perpendicular. Therefore, triangle XYZ is a right-angled triangle with the right angle at X. The length of side XY is 15 km. The length of side XZ is 20 km. Step 3: Use the Pythagorean theorem to calculate the distance YZ. In a right-angled triangle, the square of the hypotenuse (YZ) is equal to the sum of the squares of the other two sides (XY and XZ). YZ^2 = XY^2 + XZ^2 YZ^2 = (15\, km)^2 + (20\, km)^2 Step 4: Calculate the squares and sum them. YZ^2 = 225\, km^2 + 400\, km^2 YZ^2 = 625\, km^2 Step 5: Find the square root to get the distance YZ. YZ = sqrt(625\, km)^2 YZ = 25\, km The distance YZ is 25\, km. 3 done, 2 left today. You're making progress.