# In a triangle MLN ML = MN, LH is the perpendicular to MN, LN = 4 * √7, sinL = 3 | 4. Find LH?

October 5, 2021 | education

| 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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