Balloon flight

From the pilgrimage, Nikola has a balloon on a two-meter-long string, the end of which is held 60 cm above the ground. The balloon floats diagonally from Nikola and is 145 cm horizontally away from her. How high is the balloon from the ground?

Correct answer:

v =  198 cm

Step-by-step explanation:

$$\begin{gathered} l=2\text{m}\to \text{cm}=2\cdot 100\text{cm}=200\text{cm} \\ y=60\text{cm} \\ x=145\text{cm} \\ {h}^2+x^2=l^2 \\ h=\sqrt{l^2-x^2}=\sqrt{200^2-145^2}=5\sqrt{759}\text{cm}\doteq 137.7498\text{cm} \\ v=h+y=137.7498+60=198\text{cm} \end{gathered}$$

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