Asked by annie

A rhombus ABCD has AB = 10 and m∠A = 60°. Find the lengths of the diagonals of ABCD.
Answered by plumpycat
A rhombus has four sides equal in length and opposite sides parallel. Opposite interior angles are equal. Also, the diagonals bisect the interior angles.
Try constructing a rough sketch of a rhombus with a pencil and ruler. Label all 4 sides with"10" and two opposite angles 60 degrees (choose the two acute angles for this). You should be able to figure out the other two opposite angles. Draw in the diagonals, and you should have enough information to use the cosine law to find their lengths.

Answered by SmartNerd
Answer smart boy >:-(

Answered by bob
123456
Answered by bob
1234567890
Answered by Morning
Its Actually 10 and 10√3
Answered by Mr.Hunt
its 5 square root 7
Answered by Hope This Helps!
Three important properties of the diagonals of a rhombus that we need for this problem are:
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus

First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°.

Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.

For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.





Similarly, we have





Now, to find the lengths of the diagonals,




So, the lengths of the diagonals are 10 and 10√3.

Answer: 10 and 10√3 units
Answered by average
THX
Answered by Hope This Helps!
Thanks for all the likes you guys are so nice!
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