Question

dawns work
line 1: a = 20 - 5 = 15
line 2: 15² + b² = 50²
dawns work to set up the problem is shown. is she correct? if not, explain her mistake.
dawn is incorrect. in line 2, the equation should be 5² + 20² = b².
dawn is incorrect. in her sketch, 50 meters should be written along the leg of the triangle.
dawn is incorrect. in line 2, the equation should be 20² + x² = 50².
dawn is correct.

Explanation:

Dawn made two mistakes. First, the side labeled 20 is not the hypotenuse; the hypotenuse is the longest side (50), so the leg length should not be calculated as 20 - 5 = 15. Second, the Pythagorean theorem states that the sum of the squares of the legs equals the square of the hypotenuse, so the correct equation should involve the unknown leg (let’s call it \(x\)): \(5^2 + x^2 = 50^2\) (or similar with the correct leg labels). The option indicating she is incorrect and the equation should be \(20^2 + x^2 = 50^2\) aligns with identifying the hypotenuse correctly.

Answer:

Dawn is incorrect. In Line 2, the equation should be \(20^2 + x^2 = 50^2\).