The angles of a triangle are 1: 1: 2 and the longest side is 13. Find the height drawn to this side.
August 28, 2021 | education|
Let the angle BAC = X0, the angle ACB = X0, then the angle ABC = 2 * X0.
The sum of the interior angles of the triangle is 180, then (X + X + 2 * X) = 180.
4 * X = 180.
X = 180/4 = 45.
Angle BAC = ACB = 45.
Angle ABC = 2 * 45 = 90.
Then the triangle ABC is rectangular and isosceles, and the height BH is also the median of the triangle ABC. Then AH = CH = AC / 2 = 13/2 = 7.5 cm.
In a right-angled triangle ABН, the angle BAН = 45, then the legs of this triangle are equal.
BH = AH = 7.5 cm.
Answer: The height of the triangle is 7.5 cm.
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