In the triangle ABC ÐC = 90 °, AC = 12 cm, BC = 16 cm, CM – height. A straight line SC is drawn through vertex C

| September 14, 2021 | education

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

By the Pythagorean theorem, we find the hypotenuse AB = √ (CA ^ 2 + CB ^ 2) = √ (144 + 256) = 20.

Find the height of this triangle from the formula for the area of ​​a triangle:

S = 1/2 * AB * CM, hence CM = 2S / AB.

Now we find the area of ​​the triangle from the formula:

S = 1/2 * AC * CB = 1/2 * 12 * 16 = 96.

Then CM = 2 * 96/20 = 9.6 (cm).

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 KSM 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) = √ (KS ^ 2 + 9.6 ^ 2) = √ (KS ^ 2 + 92.16).

Answer: KM = √ (KS ^ 2 + 92.16).



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.