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

bystudin | 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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