Question

In a rhombus, the sides are 14 inches long. Two intersecting sides form a 60° angle. What are the exact lengths of the two doagonals?

Answer 1

Long Diagonal = Square Root [ 2•Side² + 2•Side² • cos(A)]

Long Diagonal = Square Root [2*14^2 + 2*14^2 * cos (60)]

Long Diagonal = Square Root [ 392 + 392*.5]

Long Diagonal = Square Root [ 588 ]

Long Diagonal =  24.248711306

Short Diagonal = Square Root [ 2•Side² - 2•Side² • cos(A)]

Short Diagonal = Square Root [ 392 -392*.5]

Short Diagonal = Square Root [ 196 ]

Short Diagonal = 14