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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