The bases of a trapezoid are 425 feet and 250 feet respectively. The angles that the sides make with the longer base are 64 degree and 75 degree. What are the sides of the trapezoid?

1 Answer
Apr 25, 2018

AD=257.3 feet and BC=239.5 feet

Explanation:

The trapezium ABCD is shown in the diagram below, where we have also drawn DL and CM perpendicular to AB as shown. Further, height of trapezium is h

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Now as (AL)/h=cot64^@ and (BM)/h=cot75^@

i.e. AL+BM=h(cot64^@+cot75^@)

But AL+BM=425-250=175

Hence, h=175/(cot64^@+cot75^@)

= 175/(0.4887+0.2679)

= 175/0.7566=231.3 feet

and as h/(AD)=sin64^@ and h/(BC)=sin75^@

i.e. AD=h/sin64^@=231.3/0.8988=257.3 feet and

BC=h/sin75^@=231.3/0.9659=239.5 feet.