In the triangle ABC AC = BC = 2√3, angle C = 120 find the height AH
October 10, 2021 | education
| Since the two sides are equal, it means that the triangle is isosceles;
The height АН forms a right angle to the BC side;
Angle A = B;
Since C = 120 °, it means;
Angle A + B = 180 ° – 120 ° = 60 °;
Angle B = 60 ° / 2 = 30 °;
Triangle ANV rectangular with right angle N.
HAB angle = 180 ° – 90 ° – 30 ° = 90 ° – 30 ° = 60 °;
From the property of a right-angled triangle, a leg lying opposite an angle of 30 ° is equal to half of the hypotenuse.
SK – height ABC.
cos60 = AK / AC;
AK = 2√3 * 1/2 = √3;
AB = 2√3;
VN = 2√3 / 2 = √3;
AH = √ (AB2 – BH2) = √ ((2√3) 2 – √32) = √ (4 * 3 – 9) = √ (12 – 9) = √3.
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