# 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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