Right triangle

A circle with a radius of 5 cm is described in a right triangle with a 6 cm leg. What is the height at the hypotenuse of this triangle?

Correct answer:

h =  4.8 cm

Step-by-step explanation:

$$\begin{gathered} a=6\text{ cm } \\ R=5\text{ cm } \\ c=2\cdot R=2\cdot 5=10\text{ cm } \\ b=\sqrt{c^2-a^2}=\sqrt{10^2-6^2}=8\text{ cm } \\ S={\displaystyle \frac{a\cdot b}{2}}={\displaystyle \frac{6\cdot 8}{2}}=24{\text{cm}}^2 \\ S={\displaystyle \frac{c\cdot h}{2}} \\ h=2\cdot S\mathrm{/}c=2\cdot 24\mathrm{/}10={\displaystyle \frac{24}{5}}={\displaystyle \frac{24}{5}}\text{ cm}=4.8\text{ cm} \end{gathered}$$

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