Triangle abs. Height H is drawn from angle A. Angle HAC = 60. AB = 4, AC = 6 Find AH.

After holding the height AH in triangle ABC, we have formed a new right-angled triangle AHC. His angle AHC is straight, because the height forms this right angle with the side BC.
We also know one more of the corners of the new triangle. The problem says that it is equal to 60 °. It remains to find the third angle HCA:
∠ HCA = 180 ° – 90 ° – 60 ° = 30 °.
Using the trigonometric rule, we can find the ratio of the leg AH to the hypotenuse AC. And all this is equal to sin 30 °, that is, 1/2:
AH: AC = 1/2;
AH * 2 = 6 * 1;
2AH = 6;
AH = 6: 2;
AH = 3 (cm).
ANSWER: AH = 3 cm.