SOLUTION: The sides of a rectangle are 10 and 16. Find, to the nearest degree, one of the smaller angles formed at the intersection of the diagonals. My work: {{{10^2 + 16^2 = x^2}}} {{{x

Algebra ->  Rectangles -> SOLUTION: The sides of a rectangle are 10 and 16. Find, to the nearest degree, one of the smaller angles formed at the intersection of the diagonals. My work: {{{10^2 + 16^2 = x^2}}} {{{x      Log On


   

Question 79650: The sides of a rectangle are 10 and 16. Find, to the nearest degree, one of the smaller angles formed at the intersection of the diagonals.
My work: 10%5E2+%2B+16%5E2+=+x%5E2 x+=+2sqrt%2889%29
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The sides of a rectangle are 10 and 16. Find, to the nearest degree, one of the smaller angles formed at the intersection of the diagonals.
My work: 10^2 + 16^2 = x^2 x = 2sqrt(89)
:
You correctly found the length of the diagonal, however they are asking for the
smaller angle formed by the diagonals.
:
Drawinging this out would help make it understandable
:
Find one angle (A) of the right triangle using the tangent
Tan(A) = 10/16
A = 32 degrees
:
That would make the two equal angles in the isosceles triangle, formed by the short side (10) and two halves of the diagonals: 90 - 32 = 58 degrees;
Subtract those two angles from 180 - 58 - 58 = 64 degrees is the smaller angle
formed by the two diagonals.
:
Hope this made sense