Voltage 2533

The high voltage mast fastens 30 m long ropes at 2/3 of the mast height. How tall is the mast if the ropes anchor at 15 m from the mast?

Correct answer:

x =  38.9711 m

Step-by-step explanation:

$$\begin{gathered} c=30\text{m} \\ a=15\text{m} \\ {c}^2=a^2+b^2 \\ b=\sqrt{c^2-a^2}=\sqrt{30^2-15^2}=15\sqrt{3}\text{m}\doteq 25.9808\text{m} \\ b=\frac{2}{3}\cdot x \\ x=\frac{3}{2}\cdot b=\frac{3}{2}\cdot 25.9808=38.9711\text{m} \end{gathered}$$

Try another example