[ENEM 2023] 148 📘 PERCENTAGE A flagpole was installed perpendicular to the ground in a

[148]A flagpole was installed perpendicular to the ground in a flat region. Due to the strong winds, three steel cables of the same length will be installed to support the mast. Each steel cable will be perfectly stretched, with one end at a point P on the mast, at a height h from the ground, and the other end, at a point on the ground, as shown in the figure.
The steel cables form an angle α with the floor plane.
For security reasons, there are only three installation options:
alternative I: h = 11 m and α = 30°
option II: h = 12 m and α = 45°
option III: h = 18 m and α = 60°
The option to be chosen is the one in which the cables are as small as possible.
What will be the size, in meters, of each of the cables to be installed?
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ENEM 2023 - Mathematics Test Solved by Prof. Cashew.
Question 148 of the Blue Test - ENEM 2023
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