How do I solve for the variables of the figures given here?

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1 Answer
Jan 20, 2018

Figure C #-# #x=6sqrt3# and #y=18#
Figure D #-# #x=8sqrt6# and #y=8sqrt3#

Explanation:

Figure C #-# In a right angled triangle, if one acute angle is #60^@#, the triangle's angles are #30^@,60^@# and #90^@#. In such a triangle the largest side, the hypotenuse is double the smallest side, which is opposite the smallest angle of #30^@#.

As hypotenuse is #12sqrt3#, the smallest side #x=(12sqrt3)/2=6sqrt3# and the third side is always #sqrt3#-times te smallest side and hence #y=6sqrt3xxsqrt3=6xx3=18#.

Figure D #-# In a right angled triangle, if one acute angle is #45^@#, the other acute angle too is #45^@# and we have a right angles isosceles triangle. As such both smaller sides are equal and diagonal is #sqrt2#-times the smaller side.

Hereone smaller side is #8sqrt3# and other smaller side too is #8sqrt3# i.e. #y=8sqrt3# and hypotenuse is #8sqrt3xxsqrt2=8sqrt6# and hence #x=8sqrt6#.