In triangle ABC, angle C is 90, angle A is 30. AB 88 √3. Find the height CH.

univerkov | May 25, 2021 | education

In a right-angled triangle, the cosine of its acute angle is the ratio of the length of the adjacent leg to the length of the hypotenuse.

Then, in a right-angled triangle ABC:

CosBAC = AC / AB.

AC = AB * CosBAC = 88 * √3 * √3 / 2 = 132 cm.

Determine the area of the triangle ABC.

Savs = AB * AC * SinBAC / 2 = 88 * √3 * 132 * (1/2) / 2 = 2904 * √3 cm2.

So Savs = AB * CH / 2.

СН = 2 * Saс / AB = 2 * 2904 * √3 / 88 * √3 = 66 cm.

Answer: The length of the CH height is 66 cm.

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