In the triangle ABC ÐC = 90 °, AC = 12 cm, BC = 16 cm, CM is the bisector.

| September 14, 2021 | education

In the triangle ABC ÐC = 90 °, AC = 12 cm, BC = 16 cm, CM is the bisector. A straight line SC is drawn through vertex C, perpendicular to the plane of the triangle ABC. Find KM.

Consider a right-angled triangle ABC, where ∟C = 90 °, AC = 12 cm, BC = 16 cm, CM is the bisector.

By the Pythagorean theorem, the hypotenuse AB = √ (CA ^ 2 + CB ^ 2) = √ (144 + 256) = 20 (as in the first problem).

Find the bisector of a right-angled triangle by the formula:

CM = 2 * AC * CB * cos450 / (AC + CB) = (2 * 12 * 16 * √2 / 2) / (12 + 16) = (48√2) / 7.

Now, to the plane of this triangle from the vertex C, we draw a segment CK, perpendicular to the plane of the triangle. So we get that the KCM triangle is rectangular, where KM is the hypotenuse. In order to find the CM, you need to know the segment of the CC.

And since it is not specified, the solution is obtained in general form:

KM = √ (KS ^ 2 + CM ^ 2) = √ (KC ^ 2 + ((48√2) / 7) ^ 2) ≈ √ (KS ^ 2 + 95.2 ^ 2).

Answer: KM = √ (KS ^ 2 + 95.22).



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