The angle at the apex opposite to the isosceles triangle is 150 degrees. The side of the triangle is 13. Find the area of this triangle.
BH-height drawn from the top of an isosceles triangle. ВН is also both the median and the bisector.
<AВН = <СВН = 150: 2 = 75о.
Triangles AВН and СВН are equal (side ВН is common, AB = СВ by condition).
SАВС = SАВН + SСВН = 2 * SАВН = 2 * 1/2 * АН * ВН = АН * ВН.
AH = AB * cosВAН = AB * cos (90 – 75) = AB * cos 15.
HВ = AB * cosABН = AB * cos75.
SABC = AB * cos15 * AB * cos75 = AB2 * 1/2 * (cos (75 – 15) -cos (75 + 15)) = 169 * 1/2 * 1/2 = 42.25.
Answer: the area is 42.25.
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