Question

In Quadrilateral ABCD, B = D = 90, C = 120◦ . If AB = 4, AD = 3 find BC and CD. Solve without Trigonometry and Solve using 30-60-90 Triangle​

Answer 1

Given  : In Quadrilateral ABCD, ∠B = ∠D = 90°, ∠C = 120° .  

If AB = 4, AD = 3

To  find  : BC and CD.  

Solution:

In Quadrilateral ABCD, ∠B = ∠D = 90°,

∠B + ∠D = 180°

  ∠C = 120°.  

=>   ∠A = 60°

Extend  DC to cut Extended AB  at E

in ΔADE  , ∠D = 90°  

AD = 3    ∠A = 60°

=>  AE = 6   AE = AB + BE  = 4 + BE  => BE =  2

    DE = 3√3

Now in Δ CBE   ∠B = 90°  

BE = 2    ∠E = 30°

BC = 2/√3  = 2√3/3  = 1.155

CE = 4/√3  = 4√3/3

CD = DE - CE

=> CD = 3√3 - 4√3/3  =  5√3/3 = 2.887

BC = 2√3/3  = 1.155

CD = 5√3/3  = 2.887

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