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
Shwetank Mauria
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#

enter image source here

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.

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