Question

find the height h of the right triangle abc shown in the figure. hint: find the area of triangle abc in two different ways.

Explanation:

Step1: Calculate area via legs

The triangle is right - angled at \(C\), so legs are \(15\) and \(20\). Area \(A=\frac{1}{2}\times15\times20\)
\(A = 150\)

Step2: Let hypotenuse be \(AB\), find \(AB\)

By Pythagorean theorem, \(AB=\sqrt{15^{2}+20^{2}}=\sqrt{225 + 400}=\sqrt{625}=25\)

Step3: Calculate height \(h\)

Now, area can also be \(A=\frac{1}{2}\times AB\times h\). We know \(A = 150\) and \(AB = 25\), so \(\frac{1}{2}\times25\times h=150\)
\(25h=300\)
\(h = 12\)

Answer:

\(12\)