Question

solve for the missing sides.
1)
ad = _______ ac = _____ ab = _______
2)

Explanation:

Step1: Use the geometric mean theorem (altitude-on-hypotenuse theorem)

For a right - triangle \(ABC\) with altitude \(AD\) to the hypotenuse \(BC\), \(AD=\sqrt{CD\times BD}\). Given \(CD = 3\) and \(BD=10\), then \(AD=\sqrt{3\times10}=\sqrt{30}\).

Step2: Use the geometric mean theorem for \(AC\)

\(AC=\sqrt{CD\times BC}\). Since \(BC=CD + BD=3 + 10 = 13\), then \(AC=\sqrt{3\times13}=\sqrt{39}\).

Step3: Use the geometric mean theorem for \(AB\)

\(AB=\sqrt{BD\times BC}\). With \(BC = 13\) and \(BD = 10\), then \(AB=\sqrt{10\times13}=\sqrt{130}\).

Answer:

\(AD=\sqrt{30}\), \(AC=\sqrt{39}\), \(AB=\sqrt{130}\)