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Find the area of the shaded square.... with solution. |
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Answer» Answer: 90.25 Step-by-step explanation: You have to USE trigonometry for this. In the upper Big TRIANGLE ABC right angled at B. tan A(the one on the left side) = 15/5 = 3 tan A = 3 A = 72 degrees C = 18 degrees In the smaller triangle on the right top DEC right angled at E Angle C = 18 degrees sin C = DE/DC sin 18 = DE/DC 0.3 = DE/5 DE = 1.5 units WE can assume that all small triangles are congruent. EC = 4.8(Using pythagoras theorem) The four lines which are intercepting to create the SQUARE are equal to 5* root(10).( Using pythagoras theorem for the bigger triangles.) DE is the small PART of the big line . Similarly the other part is equal to EC since the triangles are congruent. Therefore, side of smaller square = 5 root(10) - (1.5 + 4.8) side of smaller square = 15.8 - 6.3 side of smaller square = 9.5 area of smaller square = side^2 = 9.5^2 = 90.25 sq.units
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