# In an isosceles triangle ABC, the base is 12 cm, and the height drawn to the base is 8 cm. Find the median to the side.

July 28, 2021 | education

| The height AD of an isosceles triangle is also the median of this triangle, then BD = CD = BC / 2 = 12/2 = 6 cm.

In a right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AD ^ 2 + CD ^ 2 = 64 + 36 = 100.

AC = 10 cm.

Determine the cosine of the angle ACD.

CosACD = CD / AC = 6/10 = 0.6.

BE is the median of the triangle, then AE = CE = AC / 2 = 10/2 = 5 cm.

In a triangle BCE, we apply the cosine theorem to determine the side BE.

BE ^ 2 = BC ^ 2 + CE ^ 2 – 2 * BC * CE * CosBCE = 144 + 25 – 2 * 12 * 5 * 0.6 = 169 – 72 = 97.

BE = √97 cm.

Answer: The length of the median BE is equal to √97 cm.

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