A straight line a is drawn through the vertex of an acute angle A of a right-angled triangle ABC (^ B = 90) perpendicular to the plane

A straight line a is drawn through the vertex of an acute angle A of a right-angled triangle ABC (^ B = 90) perpendicular to the plane of the triangle. Find the distance between lines BC and a if BC = 10 cm and AC = 26 cm.

Since the straight line “a” is perpendicular to the plane of the triangle, and the triangle ABC is rectangular with a right angle B, the shortest distance from the straight line “a” to the side BC will be the leg AB of the triangle.

By the Pythagorean theorem AB ^ 2 = AC ^ 2 – BC ^ 2 = 26 ^ 2 – 10 ^ 2 = 676 – 100 = 576.

AB = 24 cm.

Answer: The distance between lines BC and “a” is 24 cm.