In a triangle MNK MN = 10, NK = 17. MK = 21. NF is the height of the triangle; PN – perpendicular

| June 17, 2021 | education

In a triangle MNK MN = 10, NK = 17. MK = 21. NF is the height of the triangle; PN – perpendicular to the MNK plane. Find the distance from point P to the side of triangle MK if NP = 15.

Knowing the lengths of the sides of the triangle MNK, we define the plane of the triangle.

S = √ (p (p – MN) * (p – MK) * (p – NK).

Where p is the semi-perimeter of the triangle.

p = (10 + 17 + 21) / 2 = 48/2 = 24.

S = √ (24 * (24 – 17) * (24 – 21) * (24 – 10)) = √24 * 7 * 3 * 14 = 84.

Determine the height NL of the triangle MNK.

S = (MK * NL) / 2.

84 = 21 * NL / 2.

NL = 84 * 2/21 = 8 cm.

Determine the distance from point P to line MK.

In the triangle PLN, the angle N is a straight line, we find PL by the Pythagorean theorem.

PL ^ 2 = PN ^ 2 + NL ^ 2 = 15 ^ 2 + 8 ^ 2 = 289.

PL = 17 cm.

Answer: PL = 17 cm.



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