# In a triangle, the two sides are 5 and 6 cm, and the sine of the angle between them is 0.8.

In a triangle, the two sides are 5 and 6 cm, and the sine of the angle between them is 0.8. Find the median drawn to the larger side?

Determine the cosine of the angle BAC.

Cos2BAC = 1 – Sin2BAC = 1 – 0.64 = 0.36.

CosBAC = 0.6.

By the cosine theorem, we determine the length of the BC side.

BC ^ 2 = AC ^ 2 + AB ^ 2 – 2 * AC * BC * CosBAC = 36 + 25 – 2 * 6 * 5 * 0.6 = 61 – 36 = 25.

BC = 5 cm.

AB = BC = 5 cm, then the ABC triangle is isosceles, and its large side AC is its base.

The median BH is also the height of the ABC triangle. In a right-angled triangle ABH, according to the Pythagorean theorem, BH ^ 2 = AB ^ 2 – AH ^ 2 = 25 – 9 = 16.

BH = 4 cm.

Answer: The length of the medians BH is 4 cm.

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