In the triangle ABC C = 90 ° CH, the height is A = 30 ° AB = 24. find BH.

Let us determine what the side CB will be equal to, when from the condition of the task we know that the length of the hypotenuse AB is 24, while the angle A is 30 °:

CB / AB = sin A;

CB = 24 * 1/2 = 12.

Let’s determine what the angle B of our triangle will be equal to:

90 – 30 = 60.

Let us determine what the height of the CH will be equal to, which lies opposite the angle of 60 °:

CH / CB = sin B;

CH = 12 * √3 / 2 = 6√3.

Let us determine what the length of the VN will be equal to:

√ (12 ^ 2 – (6√3) ^ 2) = √ (144 – 108) = √36 = 6.

Answer: The HV length will be 6.