Question

∠c is a
ex. 11–20
if db = 8 and
ab = 18, find ac

Explanation:

Step1: Find the length of AD

Since \(AB = 18\) and \(DB=8\), then \(AD=AB - DB\).
\(AD = 18 - 8=10\)

Step2: Use the geometric mean theorem (altitude - on - hypotenuse theorem)

In a right - triangle \(ABC\) with altitude \(CD\) to hypotenuse \(AB\), the formula \(AC^{2}=AD\times AB\) holds.
Substitute \(AD = 10\) and \(AB = 18\) into the formula: \(AC^{2}=10\times18 = 180\)

Step3: Solve for AC

Take the square root of both sides. Since \(AC>0\), \(AC=\sqrt{180}\)
Simplify \(\sqrt{180}=\sqrt{36\times5}=6\sqrt{5}\)

Answer:

\(6\sqrt{5}\)