In an isosceles triangle ABC (AB = BC), the base angle is 75 degrees. Find the length of the height AH if the side length is 7.

| February 6, 2021 | education

First way.

Since, by condition, AB = BC, the triangle ABC is isosceles, and then the angles at its base are equal.

Angle BAC = BCA = 750, then angle ABC = (180 – 75 – 75) = 30.

Let’s define the area of ​​the triangle ABC.

Savs = AB * BC * Sin30 / 2 = 7 * 7 * (1/2) / 2 = 49/4 = 12.25 cm2.

Let us determine the area of ​​the triangle through the side of the BC and the height AH.

Sаvs = ВС * АН / 2.

AH = 2 * Savs / BC = 2 * 12.25 / 7 = 3.5 cm.

Second way.

The ABC triangle is isosceles, then the angle BAC = BCA = 75. The angle ABC = (180 – 75 – 75) = 30.

AH is height, then triangle ABН is rectangular, and leg AH is located opposite angle 30, which means its length is equal to half the length of the hypotenuse AB.

AH = AB / 2 = 7/2 = 3.5 cm.

Answer: The length of the height AH is 3.5 cm.



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