An oblique FK is drawn from point F to the alpha plane. Find the distance from point F

An oblique FK is drawn from point F to the alpha plane. Find the distance from point F to the alpha plane if FK = 17 cm, and the length of the FK projection onto the alpha plane is 8 cm.

The distance from point F to plane Α is the perpendicular to FH. The FK projection onto the plane will be the NK segment. Thus, a triangle FHK is formed with a right angle H, legs FH and HK = 8 cm, hypotenuse FK = 17 cm.
By the Pythagorean theorem, we find the distance from the point F to the plane Α:
FK ^ 2 = FH ^ 2 + HK ^ 2;
FH ^ 2 = FK ^ 2 – HK ^ 2;
FH = √ (FK ^ 2 – HK ^ 2);
FH = √ (17 ^ 2 – 8 ^ 2) = √ (289 – 64) = √225 = 15 (cm).
Answer: FH = 15 cm.