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 hypotenuse of the right-angled triangle. Given the opposite side is 3 cm and the adjacent side is 4 cm. Using the Pythagorean theorem, a^2 + b^2 = c^2, where c is the hypotenuse. hypotenuse = sqrt((opposite))^2 + (adjacent)^2 hypotenuse = sqrt((3 cm))^2 + (4 cm)^2 hypotenuse = sqrt(9 cm)^2 + 16 cm^2 hypotenuse = sqrt(25 cm)^2 hypotenuse = 5 cm Step 2: Calculate . The definition of in a right-angled triangle is the ratio of the length of the opposite side to the length of the hypotenuse. = oppositehypotenuse = 3 cm5 cm = (3)/(5) Step 3: Compare with the given options. The calculated value (3)/(5) matches option C. The final answer is C. --- Step 1: Convert the actual distance to centimeters. The map distance is 12 cm. The actual distance is 36 km. We know that 1 km = 1000 m and 1 m = 100 cm. Therefore, 1 km = 1000 × 100 cm = 100,000 cm. So, 36 km = 36 × 100,000 cm = 3,600,000 cm. Step 2: Express the scale as a ratio of map distance to actual distance. The scale is given by: Scale = Map distance : Actual distance Scale = 12 cm : 3,600,000 cm Step 3: Simplify the ratio to the form 1:N. Divide both sides of the ratio by 12: Scale = (12)/(12) : (3,600,000)/(12) Scale = 1 : 300,000 Step 4: Compare with the given options. The calculated scale 1:300000 matches option A. The final answer is A.