# Find the base of an isosceles triangle if the base angle is 30 degrees and the height to the base is 10 Find the base.

August 31, 2021 | education

| Given:

isosceles triangle ABC,

ВН – height,

BH = 10,

angle A = angle BC = 30 degrees.

Find the base of the speaker -?

1) Consider a right-angled triangle ABН. In a right-angled triangle opposite an angle of 30 degrees lies a leg, which is half the hypotenuse. Then

BH = 1/2 * AB;

AB = 2 * BH;

AB = 2 * 10;

AB = 20.

2) By the Pythagorean theorem:

AH ^ 2 + HB ^ 2 = AB ^ 2;

AH ^ 2 = AB ^ 2 – HB ^ 2;

AH ^ 2 = 400 – 100;

AH ^ 2 = 300;

AH = 10√3:

3) In an isosceles triangle, the height is also the median, then

AC = 2 * AH;

AC = 2 * 10√3;

AC = 20√3

Answer: 20√3.

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