In triangle CDE, angle C = 30 °, angle D = 45 °, CE = 5√2. find DE.

univerkov | August 9, 2021 | education

Let’s build the height ЕН. In a right-angled triangle CEН, the leg EH lies opposite the angle 30, then EH = EC / 2 = 5 * √2 / 2 cm.

The EDH triangle is rectangular and isosceles since the angle EDH = 45, then 2 * EH ^ 2 = ED ^ 2 = 2 * 25 * 2/4 = 25.

ED = 5 cm.

Answer: The length of the segment DE is 5 cm.

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