Concept Check Work each problem.
Construct an equilateral triangle with each side having length 2k.
(a) What is the measure of each angle?
(b) Label one angle A. Drop a perpendicular from A to the side opposite A. Two 30° angles are formed at A, and two right triangles are formed. What is the length of the sides opposite the 30° angles?
(c) What is the length of the perpendicular in part (b)?
(d) From the results of parts (a) – (c), complete the following statement: In a 30°– 60° right triangle, the hypotenuse is always _______ times as long as the shorter leg, and the longer leg has a length that is ______ times as long as that of the shorter leg. Also, the shorter leg is opposite the ________ angle, and the longer leg is opposite the _______ angle.
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