An oblique is drawn from point A to the plane, the length of which is 10 cm.

An oblique is drawn from point A to the plane, the length of which is 10 cm. Find the length of the perpendicular if the length of the projection of this oblique onto the plane is 6 cm.

In fact, the oblique, drawn from point A to the plane, is the hypotenuse with = 10 cm, the projection of this oblique is one of the legs a = 6 cm, the perpendicular is the second leg b. Using the Pythagorean theorem, we find the second leg b:
c ^ 2 = a ^ 2 + b ^ 2;
b = √ (c ^ 2 – a ^ 2);
b = √ (10 ^ 2 – 6 ^ 2) = √ (100 – 36) = √64 = 8 (cm).
Answer: b = 8 cm.