Triangle ABC is rectangular and isosceles with a right angle C and a hypotenuse of 6 cm.

| July 4, 2021 | education

Triangle ABC is rectangular and isosceles with a right angle C and a hypotenuse of 6 cm. The segment CM is perpendicular to the plane of the triangle and is equal to 5 cm. Find the distance from point M to line AB

To solve the problem, consider the figure.

Consider an isosceles right-angled triangle ABC, in which the angle C is straight, and AB = 6 cm, AC = BC.

Let us find the legs of the triangle ABC by the Pythagorean theorem.

AB ^ 2 = BC ^ 2 + AC ^ 2.

36 = 2 * AC ^ 62.

AC = √18.

Let us draw the CE height to the hypotenuse AB and find its value.

CE = AC * BC / AB = √18 * √18 / 6 = 3 cm.

Consider a right-angled triangle CME and, by the Pythagorean theorem, find the hypotenuse ME.

ME ^ 2 = CM ^ 2 + CE ^ 2 = 52 + 32 = 25 + 9 = 34.

ME = √34.

Answer: The distance from M to AB is √34 cm.



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