In a right-angled triangle, the outer angle at the vertex A is equal to 120 degrees AC + AB = 18cm find AC and AB
| February 7, 2021 | education
The sum of the outer and inner angles is 180 °. If the outside angle A is 120 °, then the inside angle A is equal to:
∠ А = 180 ° – 120 ° = 60 °.
If there is an angle of 60 ° in a right-angled triangle, then the leg adjacent to this angle is half the hypotenuse:
AB = 2AC.
It is known that:
AC + AB = 18 cm.
We express AB through AC, substitute it into the equation and solve:
AC + 2AC = 18;
3AC = 18;
AC = 18/3;
AC = 6 cm;
AB = 2AC = 2 * 6 = 12 cm.
Answer: 6 cm, 12 cm
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