In an isosceles triangle KRM one of the angles is 120 °. From the vertex M
| March 19, 2021 | education
In an isosceles triangle KRM one of the angles is 120 °. From the vertex M to the lateral side a height equal to 14 cm is drawn. Find the base of the triangle MRK.
Since the MRK triangle is isosceles with the base of the MK, the angles at its base are equal.
РМК angle = РKM.
The sum of the inner angles of the triangle is 120, then the angle РMK = РCM = (180 – MРK) / 2 = (180 – 120) / 2 = 30.
The segment MН is the height drawn to the lateral side, then the МНК triangle is rectangular, in which the angle MНC = 30.
The MH leg lies opposite an angle of 30, then its length is equal to half the length of the MK hypotenuse.
MН = MK / 2.
MK = 2 * MH = 2 * 14 = 28 cm.
Answer: The length of the base of the triangle is 28 cm.
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