RT triangle and height

Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.

Correct answer:

a =  3 cm
c =  5 cm

Step-by-step explanation:

$$\begin{gathered} b=4 \\ h=2.4 \\ {b}^2=c_1^2+h^2 \\ {c}_1=\sqrt{b^2-h^2}=\sqrt{4^2-2.4^2}={\displaystyle \frac{16}{5}}=3.2 \\ {c}_1{c}_2=h^2 \\ {c}_2=h^2\mathrm{/}{c}_1=2.4^2\mathrm{/}3.2={\displaystyle \frac{9}{5}}=1.8 \\ c=c_1+c_2=3.2+1.8=5 \\ a=\sqrt{c^2-b^2}=\sqrt{5^2-4^2}=3\text{ cm} \end{gathered}$$

$c=c_1+c_2=3.2+1.8=5\text{ cm}$

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