In the triangle ABC AB = 8cm, the side Bc = 12 cm, the angle of ABC = 30Gradus. BD-bisectrice ABC angle. What is the ABD Area?
Calculate the area of the ABS triangle through two sides and the angle between them.
SAВС = AB * Sun * sin30 = 8 * 12 * 1/2 = 48 cm2.
Since cd bisector angle ABС, then the angle is ABD = CBD = ABС / 2 = 30/2 = 150.
Then the area of the ABD triangle is equal to:
SABD = AB * BD * SIN15 = 8 * BD * SIN15.
The CBD triangle area is:
SCBD = Sun * AD * SIN15 = 12 * AD * SIN15.
Find the attitude of the ABD and CBD triangles.
SABD / SCBD = 8/12 = 2/3.
SABD = 2 * SCBD / 3.
SABC = SABD + SCBD = 5 * SCBD / 3.
5 * SCBD = 3 * 48.
SCBD = 28.8 cm2.
SABD = SABC – SСВD = 48 – 28.8 = 19.2 cm2.
Answer: The ABD triangle area is 19.2 cm2.
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