Question 1089898
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<pre>
Use the law of cosine to find cosine of the angle between the adjacent sides:

{{{25^2}}} = {{{12^2}}} + {{{17^2}}} - {{{2*12*17*cos(alpha)}}}  ====>

{{{cos(alpha)}}} = {{{(625 - 144 - 289)/(-2*12*17)}}} = {{{-8/17}}}.


    In particular, the angle {{{alpha}}} is obtuse.


Then find {{{sin(alpha)}}} = {{{sqrt(1-cos^2(alpha))}}} = {{{sqrt(1-(-8/17)^2)}}} = {{{sqrt((289-64)/289)}}} = {{{sqrt(225)/17}}} = {{{15/17}}}.


Now, the area of the parallelogram is the product of the dimensions of two adjacent sides by the sine of the concluded angle


Area = {{{12*17*(15/17)}}} = 12*15 = 180 cm^2.
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To find the altitude of the parallelogram, divide its area by the base length.


Solved.