The height CD of triangle ABC divides side AB into segments AD and BD, so AD = 8cm, BD = 12cm.

univerkov | January 13, 2021 | education

The height CD of triangle ABC divides side AB into segments AD and BD, so AD = 8cm, BD = 12cm. Find the area of the triangle ABC if the angle is A = 60 degrees.

Consider a right-angled triangle of ACD, in which the angle of CD, by condition, is 600.
Then tg600 = CD / BP.
CD = AD * tg60 = 8 * √3 cm.
Determine the length of the side AB. AB = BP + DD = 8 + 12 = 20 cm.
Determine the area of the triangle.
Savs = AB * CD / 2 = 20 * 8 * √3 / 2 = 80 * √3 cm2.
Answer: The area of the triangle is 80 * √3 cm2.

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