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Ella selects a tile for her backsplash that is in the shape of a rhombus. Each side of the rhombus measures 4 inches. The diagonal opposite the smaller angle is 2.9 inches.

What is the measure of the larger angle in the rhombus?

approximately 118.4°

approximately 131.6°

approximately 137.5°

approximately 147.4°

 Feb 26, 2020
 #1
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We can use  the Law of Cosines to find the measure  of  the  smaller angle, A

 

2.9^2  = 4^2  + 4^2  - 2 (4)(4) cos  A

 

[2.9^2 - 4^2  - 4^2  ]  / [ -2 (4) (4)  ]  =  cos A

 

Using the  inverse  cosine  we  have that

 

arccos ( [2.9^2 - 4^2  - 4^2  ]  / [ -2 (4) (4)  ] )  = A  = 42.51°

 

And the larger  angle   is supplemental to this  =   180 - 42.51   =  137.49°  ≈  137.5°

 

 

cool cool cool

 Feb 26, 2020

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