In a right-angled triangle ABC with right angle C, the outside angle at apex A is 120 degrees
| February 26, 2021 | education
In a right-angled triangle ABC with right angle C, the outside angle at apex A is 120 degrees, AC + AB = 18cm. Find AC and AB.
The angle DAС and BAC are adjacent angles, the sum of which is 180.
The angle DAС + BAC = 180, then the angle BAC = 180 – DAС = 180 – 120 = 60.
Consider a right-angled triangle ABC, in which the angle BAC = 60, then the angle ABC = 180 – BAC – ACB = 180 – 60 – 90 = 30.
Then the leg AC lies against an angle of 30 and, accordingly, is equal to half the length of the hypotenuse AB.
AC = AB / 2.
By condition, AC + AB = 18 cm.
Then AC = 18 – AB.
AB / 2 = 18 – AB.
AB = 36 – 2 * AB.
3 * AB = 36.
AB = 36/3 = 12 cm.
AC = 18 – AB = 18 – 12 = 6 cm.
Answer: AC = 12 cm, AB = 6 cm.
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