Triangle ABC is rectangular and isosceles with right angle C and hypotenuse 6 cm. Segment CM is perpendicular

| June 19, 2021 | education

Triangle ABC is rectangular and isosceles with right angle C and hypotenuse 6 cm. Segment CM is perpendicular to the plane of the triangle and is equal to 4 cm. Find the distance from point M to straight line AB

Since the triangle is right-angled isosceles, the height CК is both the bisector and the median. Hence AK = ВK = AB / 2 = 6/2 = 3 (cm). Coals at the base of an isosceles triangle are equal to CAK = CВK = 45 degrees. From the CAK triangle, we find the CK leg according to the definition of the cotangent function: ctg CAK = AK / CK, CK leg = AK / ctg CAK = 3 / ctg 45 = 3/1 = 3 (cm). From the MCК triangle, according to the Pythagorean theorem, we find the hypotenuse MK ^ 2 = MC ^ 2 + CK ^ 2 = 4 ^ 2 + 3 ^ 2 = 16 + 9 = 25, MK = √25 = 5 (cm). This is the distance from point M to line AB.
Answer: 5 cm.



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