From the ratio of the opposite leg to the hypotenuse, we find the length of the leg LN of the triangle LNH.
sinL = LN / 4√7 = 3/4.
LN = 3/4 * 4√7 = 3√7.
Let us find the height LH lowered to the base of the isosceles triangle from the right-angled triangle LHN by the Pythagorean theorem.
LH = √ ((4√7) ^ 2 – (3√7) ^ 2) = √ (16 * 7 – 9 * 7) = √ 7 * 7 = 7.
Answer: LH = 7.
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