The height AM of triangle ABC divides its side BC into segments BM and MC.

The height AM of triangle ABC divides its side BC into segments BM and MC. find the segment MC if AB = 10√2cm, AC = 26. angle B = 45.

Triangle MAB – rectangular, angle B = 90 degrees. MBA angle = 45 degrees. The hypotenuse AB is known, which means that the height of AM can be found through the sine of 45 degrees.

AM = 10√2 * Sin45 = 10√2 * √2 / 2 = 10 cm.

Consider the triangle CAM, it is also rectangular, the angle of the CMA is a straight line. We know from him the hypotenuse CA = 26 cm and the leg AM. Now, by the Pythagorean Theorem, we find the side of CM.

CM = √ (CA * CA – AM * AM)

substitute the values and consider:

CM = √ (26 * 26 – 10 * 10) = √ (676-100) = √576 = 24.

The answer is 24 centimeters