Question

find the value of x. 11. a = x, b = 45, c = 53 12. a = 9, b = x, c = 41 right triangle diagram 364 florida geometry resources by chapter

Explanation:

Problem 11:

Step1: Apply Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\). Given \(a = x\), \(b = 45\), \(c = 53\), so \(x^2 + 45^2 = 53^2\).

Step2: Solve for \(x^2\)

Calculate \(45^2 = 2025\) and \(53^2 = 2809\). Then \(x^2 = 2809 - 2025 = 784\).

Step3: Find \(x\)

Take the square root: \(x = \sqrt{784} = 28\).

Problem 12:

Step1: Apply Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\). Given \(a = 9\), \(b = x\), \(c = 41\), so \(9^2 + x^2 = 41^2\).

Step2: Solve for \(x^2\)

Calculate \(9^2 = 81\) and \(41^2 = 1681\). Then \(x^2 = 1681 - 81 = 1600\).

Step3: Find \(x\)

Take the square root: \(x = \sqrt{1600} = 40\).

Answer:

Problem 11: \(x = 28\)
Problem 12: \(x = 40\)