# The tangent of the acute angle of a rectangular trapezoid is 5/3. Find its larger base if the smaller base is equal to height and equal to 40

May 31, 2020 | Education

| We introduce the notation and draw the height BE perpendicular to the CD as shown in the figure.

By condition AB = BE = 40

Then ABED is a square (all angles are straight and all sides are equal).

The triangle BCE is rectangular, therefore

by definition, tgC = BE / EC = 5/3.

40 / EC = 5/3 => EC = 40 * 3/5 = 24

DC = DE + EC

DE = AB (by definition of a square)

DC = 40 + 24 = 64

Answer: DC = 64

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