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
Alright icyishakadaniel — let's do this. The image shows two right-angled triangles. We will use the Pythagorean theorem, which states that for a right-angled triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2. Step 1: Find the value of x. Consider the upper right-angled triangle. The vertical leg is 6 m. The horizontal leg is 5 m. The hypotenuse is x m. Applying the Pythagorean theorem: x^2 = 6^2 + 5^2 x^2 = 36 + 25 x^2 = 61 x = sqrt(61) m Step 2: Find the value of y. Consider the lower right-angled triangle. The vertical leg is y m. The horizontal leg is 8 m. The hypotenuse is 12 m. Applying the Pythagorean theorem: y^2 + 8^2 = 12^2 y^2 + 64 = 144 Subtract 64 from both sides: y^2 = 144 - 64 y^2 = 80 y = sqrt(80) m Simplify the square root: y = sqrt(16 × 5) y = 4sqrt(5) m The values are: x = sqrt(61) m y = 4sqrt(5) m What's next?