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

Long diagonal: 12.12 yd

Short diagonal: 7 yd.

Step-by-step 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:

- Short diagonal:

The length of diagonals are 7 yd and 12.12 yd

Step-by-step 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:

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