# In the triangle ABC, AC = BC, AB = 24, and the angle C is 120. Find the height of AH.

July 26, 2021 | education

| Triangle ABC is isosceles by condition, the angles at the base are equal,

A = B, C = 120 °.

Find angle B, knowing that the sum of the angles in the triangle is 180 °. In our case, you can write:

2 × B + C = 180 °;

2 × B = 180 ° – 120 °;

2 × B = 60 °;

B = 60 °: 2;

B = 30 °.

The height АH is released for the continuation of the side ВС, since the angle С> 90 °.

In triangle ABH, angle AHB is a straight line, angle B = 30 °, AB = 24 cm is hypotenuse.

Find AH. The leg, lying opposite an angle of 30 °, is equal to half the hypotenuse.

AH = ½ AB.

AH = ½ × 24;

AH = 12 cm.

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