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A kite has the points A(1,3.5) , B(3,5), C(3,2.5) and D(a,b). Find the size of angle ABC.

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nmeisu | Student, Grade 11 | Honors

Posted February 11, 2013 at 4:04 AM via web

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A kite has the points A(1,3.5) , B(3,5), C(3,2.5) and D(a,b). Find the size of angle ABC.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 11, 2013 at 4:24 AM (Answer #1)

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The vertexes of the kite are at A(1,3.5) , B(3,5) and C(3,2.5). The angle ABC can be determined by using the law of cosines.

AB = `sqrt((3 - 1)^2 + (5 - 3.5)^2)` = `sqrt(4 + 2.25)` = `sqrt 6.25` = 2.5

BC = 2.5

CA = `sqrt(4+1) = sqrt 5`

`(sqrt 5)^2 = 2.5^2 + 2.5^2 - 2*2.5*2.5*cos ABC`

=> `cos ABC = 0.6`

=> `ABC = cos^-1 0.6 ~~ 53.13`

The angle ABC is approximately 53.13 degrees.

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