SOLUTION: What is The measure of angle d1 and the tangent ratio of angle c2. Parallelogram ABCD is a rhombus. Side BC = 5 cm and segment AO = 3.9 cm Parallelogram image: https://imgur.

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Question 1129857: What is The measure of angle d1
and the tangent ratio of angle c2.
Parallelogram ABCD is a rhombus. Side BC = 5 cm and segment AO = 3.9 cm
Parallelogram image: https://imgur.com/Kq6O5Nb

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

By definition, all sides of a rhombus have the same length.
Also, the diagonals are perpendicular bisectors of each other.
Because of that, the diagonals divide the rhombus into 4 congruent right triangles.
For each of those triangles, the hypotenuse is a rhombus side, of length BC=5cm ,
and one leg length is OA=OC=3.9cm .
Applying the Pythagorean theorem we can find the other length, x=OB=OD :
x%5E2%2B%283.9cm%29%5E2=%285cm%29%5E2 .
Solving for x ,
x%5E2=%285cm%29%5E2-%283.9cm%29%5E2
x%5E2=25cm%5E2-15.21cm%5E2
x%5E2=9.79cm%5E2
x=sqrt%289.79cm%5E2%29=approximately3.129cm

Taking one leg as the base and the other leg as the height,
the area of each triangle can be calculated as
%283.9cm%29%2A%283.129cm%29%2F2 ,
and the area of the rhombus (4 triangles) is
4%2A%283.9cm%29%2A%283.129cm%29%2F2=2%2A%283.9cm%29%2A%283.129cm%29=approximatelyhighlight%2824.4cm%5E2%29

The length of diagonal BD is approximately
BD=OB%2BOD=3.129cm%2B3.129cm=highlight%286.258cm%29 ,
or we could say it is approximately highlight%286.26cm%29 .