Question

a right triangle has one leg measuring 9 units and a hypotenuse of 15 units. what is the length of the missing leg in exact form?
√81 or 9
√144 or 12
√108 or 6√3
√225 or 15

Explanation:

Step1: Apply Pythagorean theorem

Let the legs be \(a = 9\), \(b\) (unknown), and hypotenuse \(c = 15\). The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). So, \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 9\) and \(c = 15\) into \(b^{2}=c^{2}-a^{2}\). Then \(b^{2}=15^{2}-9^{2}=225 - 81=144\).

Step3: Solve for \(b\)

Take the square root of both sides. \(b=\sqrt{144}\) (since length is non - negative).

Answer:

\(\sqrt{144}\text{ or }12\)