Right-angled - legs

The lengths of legs are a = 7.2 cm and b = 10.4 cm in the right-angled triangle ABC. Calculate:
a) lengths of the sections of the hypotenuse
b) height to the hypotenuse c

Correct answer:

c₁ =  4.0983 cm
c₂ =  8.5508 cm
h =  5.9198 cm

Step-by-step explanation:

$$\begin{gathered} a=7.2\text{cm} \\ b=10.4\text{cm} \\ {c}^2=a^2+b^2 \\ c=\sqrt{a^2+b^2}=\sqrt{7.2^2+10.4^2}=4\sqrt{10}\text{cm}\doteq 12.6491\text{cm} \\ {a}^2=c\cdot c_1 \\ {b}^2=c\cdot c_2 \\ {c}_1=\frac{a^2}{c}=\frac{7.2^2}{12.6491}=4.0983\text{cm} \end{gathered}$$

$c_2=\frac{b^2}{c}=\frac{10.4^2}{12.6491}=8.5508\text{cm}$

$$\begin{gathered} S=\frac{a\cdot b}{2}=\frac{c\cdot h}{2} \\ h=\frac{a\cdot b}{c}=\frac{7.2\cdot 10.4}{12.6491}\text{cm}=5.9198\text{cm} \end{gathered}$$

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