In triangle ABC, angle C is 90 degrees, CH is height, angle A is 30 degrees, AB = 26. Find CH.

| March 7, 2021 | education

It is necessary to find the length of the CH height. Angle A is equal to 30 degrees, by the property of a right-angled triangle, we know that the leg, which lies opposite the angle of 30 degrees, is equal to half of the hypotenuse. It follows that the leg BC is equal to half of the hypotenuse AB, that is, 0.5 * 26 = 13 cm.From the Pythagorean theorem the equality of the sum of the squares of the legs to the square of the hypotenuse, we calculate the leg AC as follows:

AC ^ 2 + BC ^ 2 = AB ^ 2 => AC = √ (AB ^ 2-BC ^ 2) or AC = √ (676-169) = 13√ (3) see.

Since CH is perpendicular to AB, the triangles AНС and AНС are rectangular.

In the AНС triangle, the AC is the hypotenuse and the CH-leg, lying opposite the angle A equal to 30 degrees, from which it follows that CH is equal to half of the AC or CH = 6.5 * √ (3) cm.



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