Through the vertex of the right angle of the isosceles triangle MHK, a straight line MP is drawn

Through the vertex of the right angle of the isosceles triangle MHK, a straight line MP is drawn, perpendicular to its plane. The distance from point P to line HK is 13 cm, MH is 5 roots of 2 cm. Find PM.

Since there is an isosceles right-angled triangle at the base, its angles at the base are 45. MKH = MНK = 45.

By condition, the length of МН = 5 * √2, then ME = МН * Sin 45 = 5 * √2 * √2 / 2 = 5 cm.

Consider a right-angled triangle EMP, in which the hypotenuse PE, according to the condition, is 3 cm, and the leg ME = 5 cm, then the segment PM, according to the Pythagorean tower, is equal to:

PM ^ 2 = PE ^ 2 = ME ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144.

РМ = √144 = 12 cm.

Answer: The segment PM = 12 cm.