Perpendicular 32733

Calculate the right triangle ABC, the perpendicular b = 43.5 cm of the hypotenuse c = 72.9 cm. Calculate:
A hypotenuse segment cb, side a, a hypotenuse segment ca, and a height of triangle v

Correct answer:

a =  58.4992 cm
c₁ =  46.9432 cm
c₂ =  25.9568 cm
h =  34.9069 cm

Step-by-step explanation:

$$\begin{gathered} b=43.5\text{cm} \\ c=72.9\text{cm} \\ {a}^2+b^2=c^2 \\ a=\sqrt{c^2-b^2}=\sqrt{72.9^2-43.5^2}=58.4992\text{cm} \end{gathered}$$

$$\begin{gathered} a^2=c_1\cdot c \\ {c}_1=a^2/c=58.4992^2/72.9=46.9432\text{cm} \end{gathered}$$

$$\begin{gathered} b^2=c_2\cdot c \\ {c}_2=b^2/c=43.5^2/72.9=25.9568\text{cm} \end{gathered}$$

$$\begin{gathered} h^2=c_1\cdot c_2 \\ h=\sqrt{c_1\cdot c_2}=\sqrt{46.9432\cdot 25.9568}=34.9069\text{cm} \end{gathered}$$

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