Question

How would you find the diagonals for a rhombus given the side length of 7 yds and an angle measure of 60 degrees?

Answer 1

The length of diagonals are 7 yd and 12.12 yd

Explanation:

Let the point of intersection called as 'D'

<AFD = <MFD =60/2 = 30°

Then < AFM = <AFD + <MFD

Consider the ΔAFD

The angles are 30°, 60° and 90 then sides are in the ratio

1 : √3 : 2

The two diagonals are MA and FR

MA = MD + AD = 7/2 + 7/2 = 7 yd

FR = FD + RD = 7√3/2 + 7√3/2 = 7√3 = 12.12 yd

Therefore the length of diagonals are 7 yd and 12.12 yd

Answer 2

Long diagonal: 12.12 yd

Short diagonal: 7 yd.

Explanation:

As you can see, 4 righ triangles are formed.

The larger diagonal divides the angle ∠AFM=60° into two angles of 30° each.

Then, choose one the triangles that has the angles of 30°. The hypotenuse will be the side lenght of 7 yards, the long diagonal (D) will be twice the adjacent side and the short diagonal (d) will be twice the opposite side.

Then:

- Long diagonal:

`(D)/(2)=7*cos(30\°)=6.06yd\\\\D=2((D)/(2))=2(6.06yd)=12.12yd`

- Short diagonal:

`(d)/(2)=7*sin(30\°)=3.5yd\\\\d=2((d)/(2))=2(3.5yd)=7yd`