Question

The length of each side of a rhombus is 10 and the measure of an angle of the rhombus is 60. Find the length of the longer diagonal of the rhombus.

Answer 1

Long Diagonal = side * square root (2 + 2 * cosine (smaller angle))

Long Diagonal = 10 * square root (2 + 2 * cos (60))

Long Diagonal = 10 * square root (2 + 2 * .5)

Long Diagonal = 10 * square root (2 + 1)

Long Diagonal = 10 * square root (3)

Long Diagonal = 10 * 1.7320508076

Long Diagonal = 17.320508076

Source:

1728.com/quadrhom.htm

Answer 2

The rhombus can be divided into two equilateral triangles. The longer diagonal is twice the length of the altitude of the triangle.

An equilateral triangle has an altitude that is (√3)/2×s, where s is the side length. Twice that value is s√3. Here, the side lenght is 10, so the longer diagonal is

... 10√3 ≈ 17.32