Question

semester a
what is the length of the unknown leg in the right triangle?
√134 mm
8 mm
√78 mm
6 mm

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here \(b = 7\) and \(c=\sqrt{85}\), so \(a^{2}+7^{2}=(\sqrt{85})^{2}\).

Step2: Simplify the equation

\(a^{2}+49 = 85\). Then \(a^{2}=85 - 49\).

Step3: Calculate \(a^{2}\)

\(a^{2}=36\).

Step4: Solve for \(a\)

Take the square root of both sides, \(a=\sqrt{36}\), so \(a = 6\) (since length cannot be negative).

Answer:

\(6\space mm\)