Given right triangle ABC with right angle B, angle A is twice the size of angle C. If the measure of side AB is 7 units, what is the measure of side AC?

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If angle A is twice the measure of angle C, then let angle C = x and let angle A = 2x; x + 2x + 90 = 180, 3x = 90, x = 30. The measure of angle C is 30° and the measure of angle A is 2(30) = 60°. Therefore, this is a 30-60-90 right triangle. Side AB is the shorter base, since it is the side opposite the smallest angle. The hypotenuse of a 30-60-90 right triangle is twice the length of the shorter base. Therefore, the measure of AC is 2(7) = 14 units.

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