Question

47 find the missing leg length. pythagorean theore
a = 7, c = 25
a b = 0
b b = 10
c b = 18
d b = 24

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem states that for a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse and \(a\), \(b\) are the legs. We need to solve for \(b\) when \(a = 7\) and \(c = 25\). Rearranging the formula to solve for \(b\), we get \(b^2 = c^2 - a^2\).

Step2: Substitute the given values

Substitute \(a = 7\) and \(c = 25\) into the formula: \(b^2 = 25^2 - 7^2\). Calculate \(25^2 = 625\) and \(7^2 = 49\), so \(b^2 = 625 - 49 = 576\).

Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{576}=24\).

Answer:

D. \(b = 24\)