Find the base of the isosceles triangle, the side of which is 6 cm, and one of the angles is 120 degrees.
July 28, 2021 | education|
Obviously, the angle, which is equal to 120 ° by the specification, is the angle that lies between the lateral sides.
Let’s mentally draw the height to the base. As we know from the school course, in this type of triangles it will be both the median and the bisector.
Let’s determine what each angle will equal, which is formed by dividing the initial angle by the bisector:
120: 2 = 60.
Let’s determine what half of the base will be equal to (leg in the triangle formed by the height):
6 * sin 60 ° = 6 * √3 / 2 = 3√3.
Then the base is:
3√3 * 2 = 6√3.
Answer: 6√3 cm.
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