Find the angles of an isosceles triangle if the side is 6 and its base is 6√3.

univerkov | January 11, 2021 | education

BH is the height of an isosceles triangle and is also the median.
AB and AC are the sides of the triangle, AC is the base;
AH = HC = 1/2 AC = 3 √3;
From the right-angled triangle ABN:
BH² = AB² – AH² = 36 – 27;
BH = √9 = 3;
sin A = BH / AB = 3/6 = 1/2; <A = <C = 30 °;
<B = 180 ° – 2 * 30 ° = 120 °.

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