In a right-angled triangle ABC, angle C is a straight line, angle BAC = 60 °, AB + AC = 12.

In a right-angled triangle ABC, angle C is a straight line, angle BAC = 60 °, AB + AC = 12. Find the length of the hypotenuse AB.

Determine the value of the angle ABC.

Angle ABC = 180 – BCA – BAC = 180 – 90 – 60 = 30.

Let the length of the AC leg be X cm.

The AC leg is erect against an angle of 300, then its length is equal to half the length of the hypotenuse AB.

Then AB = 2 * AC = 2 * X cm.

Since, by condition, AB + AC = 12 cm, then 2 * X + X = 12.

3 * X = 12.

X = AC = 12/3 = 4 cm.

Then AB = 2 * 4 = 8 cm.

Answer: The length of the hypotenuse AB is 8 cm.