Question 1040474
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PQRS is a parallelogram with PQ=2x cm, QR=x cm and angle PQR=110°. If the parallelogram have an area of 93.5304 cm², find the value of x. 
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Area of a parallelogram is the product of the lengths of its two adjacent sides by the sine of the angle between them:

S = x*2x*sin(110°),   or

S = {{{2x^2*sin(110^o)}}}.

(See the lesson <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Area-of-a-parallelogram.lesson>Area of a parallelogram</A> in this site).

Notice that sin(110°) = sin(180°-110°) = sin(70°).

Therefore, S = {{{2x^2*sin(70^o)}}}.

Hence, x = {{{sqrt(S/(2*sin(70^o)))}}} = {{{sqrt(93.5304/(2*sin(70^o))))}}}.

Now use your calculator and complete calculations.
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