The height BD of triangle ABC divides the base AC, into segments AD = 8 DC = 12 the angle A

univerkov | January 4, 2021 | education

The height BD of triangle ABC divides the base AC, into segments AD = 8 DC = 12 the angle A at the base is 45 °. Find the area.

1. We calculate the length of the height of the ВD through one of the trigonometric functions ∠А (tangent):
ВD: BP = tangent ∠A = tangent 45 ° = 1.
ВD = AD x 1 = 8 x 1 = 8 units.
2. AC = BP + СD = 8 + 12 = 20 units of measurement.
3. Calculate the area S of the triangle:
S = AC x ВD / 2 = 20 x 8: 2 = 80 units².
Answer: S equals 80 units².

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