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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