Find the height of an isosceles triangle if its side is 4.

Let’s build a triangle ABC-isosceles.

From the top B we draw the height BH.

The result is a triangle ABН-rectangular.

Since AB = 4 and is a hypotenuse, we find a leg AH, it is equal to half of the hypotenuse (since the leg lying opposite to one at 30 ° = half of the hypotenuse), that is, equal to 2.

Further, using the Pythagorean Theorem, we find the ВН:

AB² = AH² + BH²

BH² = AB² – AH²

BH² = 4² – 2²

BH² = 16 – 4

BH² = 12

BH = √12

BH = √4 * 3

BH = 2 * √ 3

Answer height = 2√3

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