Question

1. image of a right triangle with legs x and 24 yd, hypotenuse 30 yd 9. partially visible triangle

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(a^{2}+b^{2}=c^{2}\). Here, the hypotenuse \(c = 30\) yd and one leg \(b = 24\) yd, and we need to find the other leg \(x\).

Step2: Apply the Pythagorean theorem

Rearranging the Pythagorean theorem to solve for \(x\) (where \(x\) is a leg), we get \(x^{2}=c^{2}-b^{2}\). Substitute \(c = 30\) and \(b = 24\) into the formula:
\(x^{2}=30^{2}-24^{2}\)
First, calculate \(30^{2}=900\) and \(24^{2}=576\). Then, \(x^{2}=900 - 576=324\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{324}=18\)

Answer:

The value of \(x\) is \(18\) yards.