# In an isosceles triangle, the base angle is 30 degrees. The length of the height, lowered

March 26, 2021 | education

| **In an isosceles triangle, the base angle is 30 degrees. The length of the height, lowered to the side, is 8cm. What is the base of this triangle?**

Given:

isosceles triangle ABC,

angle A = 30 degrees,

segments AB and BC lateral sides,

AE – height,

AE = 8 centimeters.

Find the length of the base of the speaker -?

Decision:

1) Consider an isosceles triangle ABC.

His angles at the base are equal, that is, angle A = angle C = 30 degrees;

2) Consider a right-angled triangle AEC. In a right-angled triangle opposite an angle of 30 degrees lies a leg, which is half the hypotenuse. Then AE = 1/2 * AC;

AC = 2 * AE;

AC = 2 * 8;

AC = 16 centimeters.

Answer: 16 centimeters.

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