In a right-angled triangle ABC with a right angle C, the outer angle at vertex A is 120 degrees
| September 12, 2021 | education
In a right-angled triangle ABC with a right angle C, the outer angle at vertex A is 120 degrees, AC and AB is 18 cm. Find AC and AB.
Knowing the value of the external angle CAD, we determine the value of the adjacent internal angle BAC.
Angle BAC = (180 – CAD) = (180 – 120) = 60.
Then the acute angle ACD will be equal to: ABD = (180 – 90 – 60) = 30.
In a right-angled triangle ABC, leg AB lies opposite angle 30, then its length is equal to half the length of the hypotenuse AC.
AB = AC / 2.
AC = 2 * AB (1).
By condition, AB + AC = 18 cm.
Substitute equation 1.
AB + 2 * AB = 18.
3 * AB = 18.
AB = 18/3 = 6 cm.
AC = 2 * 6 = 12 cm.
Answer: The length of the AC hypotenuse is 12 cm, the AB leg is 6 cm.
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