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°
+128406 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°
