# The diagonal of a rhombus is 7cm and 10cm. Find the angles of the rhombus in two decimal places.

steveschoen | Certified Educator

The diagonals of a rhombus separate the rhombus into 4 of the same right triangles.  So, we can use trig to find each of those angles.  Then, we can find each angle of the rhombus by doubling the angles.

If the diagonals are 7 and 10, then the sides of the triangles are 3.5 and 5.  You can use trig various ways to find the angles.  I will use the inverse tangent function:

tan(-1) (3.5/5) = 34.99 degrees

tan(-1) (5/3.5) = 55.01 degrees

So, doubling those angles (I will carry all decimal places through, then round to 2 placed):

One angle is 110.02 degrees

The other angles is 69.98 degrees.

kspcr111 | Student

Please check the full solution of your question in the attachments .......

The mathematical solution for finding the angles of the rhombus is as follows . It is given in detail in the attachments below.

There are two methods in the attachments to get the solution.....please check carefully.

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 4)
This image has been Flagged as inappropriate Click to unflag
Image (2 of 4)
This image has been Flagged as inappropriate Click to unflag
Image (3 of 4)
This image has been Flagged as inappropriate Click to unflag
Image (4 of 4)