In a right-angled triangle with a hypotenuse equal to 10 and one of the legs equal to 8

| April 10, 2021 | education

In a right-angled triangle with a hypotenuse equal to 10 and one of the legs equal to 8, a bisector is drawn from an acute angle. find its length.

By the Pythagorean theorem, we determine the length of the BC leg.

BC ^ 2 = AC ^ 2 – AB ^ 2 = 100 – 64 = 36.

BC = 6 cm.

Determine the area of the triangle ABC.

Savs = AB * BC / 2 = 8 * 6/2 = 24 cm2.

The bisector ВK divides the triangle ABC into two triangles, the sum of the areas of which is equal to the area of the triangle ABC.

Savk = AB * ВK * Sin45 / 2.

Svsk = ВС * VK * Sin45 / 2.

Savs = Savk + Svsk = (AВ * ВK * Sin45 + ВC * ВK * Sin45) / 2 = ВK * Sin45 * (AB + BC) / 2.

BK = 2 * Saвс / Sin45 * (AB + BC) = 2 * 24 * 2 / √2 * 14 = 48 * √2 / 14 = 24 * √2 / 7 cm.

Answer: The length of the median ВC is 24 * √2 / 7 ≈ 4.85 cm.



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