In triangle ABC AC = BC, AD – height, angle BAD = 46. Find the corner C.
| August 12, 2021 | education
Since, by condition, AC = BC, the triangle is isosceles, which means the angle CBA = CAB.
Let the angle BAC = X, then the angle CAB = CBA = (46 – X).
In the ADC triangle, the angle is DCA = 180 – 90 – X = 90 – X.
Then the angle ACB = 180 – DCA = 180 – (90 – X) = 90 + X.
Then the sum of the angles of the triangle ABC is equal to: 180 = (46 – X) + (46 – X) + (90 + X).
X = 182 – 180 = 2.
Then ABC = 90 + 2 = 92.
Answer: Angle C = 92.
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