Triangle ABC, CD is perpendicular to plane ABC. Find the distance from point D

| September 12, 2021 | education

Triangle ABC, CD is perpendicular to plane ABC. Find the distance from point D to line AB if the angle is CAB = 90 degrees, CB = 15, AB = 9, CD = 5.

Since the base is a right-angled triangle, and the angle A has a straight line, the shortest distance from point D to AB will be the segment DA according to the theorem of three perpendiculars.

Consider a right-angled triangle ABC and find the length of the leg AC by the Pythagorean theorem.

AC ^ 2 = CB ^ 2 – AB ^ 2 = 15 ^ 2 – 9 ^ 2 = 225 – 81 = 144.

AC = 12 cm.

Since CD is perpendicular to the plane of triangle ABC, triangle CDA is rectangular with a right angle at the vertex C.

Then, by the Pythagorean theorem, we find the hypotenuse of AD.

AD ^ 2 = CD ^ 2 + AC2 = 52 + 122 = 25 + 144 = 169.

BP = 13 cm.

Answer: The distance from point D to line AB is 13 cm.



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