math problem help please. thank you?

Question

The longer sides of a parallelogram are 9 cm and 10 cm long. The longer diagonal is 15 cm. Determine the measures of the angles in the parallelogram and the length of the shorther diagonal. Thank You

Answer 1

sides of triangle form are 15 , 10 , 9
solving the angle opposite the side = 15
cos A = ( 9^2 + 10^2 - 15^2 ) / [ (2)(9)(10) ] = -0.24444444
A = 104.149 deg

solving for angle opposite side = 9
sine law
sin B = 9/15 sin A = 9/15 sin 104.149 = 0.5818
B = 35.577

solving for angle opposite side = 10
sine law
sin C = 10/15 sin A = 10/15 sin 104.149 = 0.6464
C = 40.274

A + B+ C = 180 check

interior angle of paralleogram = 104.149
. . . . . . the other angle is B+C = 75.851

solving for the other diagonal
diagonal = 9^2 + 10^2 -2 (9) (10) cos 75.851 = 137.0

Answer 2

a parallelogram has opposite sides equal
its just like a rectangle only its been skewed (or shifted sideways).

considering the four sides are 10 , 10 and 9 , 9 units....

consider the parallelogram to be made of two triangles
having sides 10 , 9 and 15 (the diagonal)
area of the triangle can be computed and is 43.634 sq units

this can be used to find the height of the triangle

area = 0.5 x base x height
take the base as 10
so u get the height to be 8.727

now when you draw the figure u will see that the angle between one set of 10 and 9 adjacent sides will be
cos inverse of 8.727/9 which is 75.85 degrees

to find the other set it will be 180-75.85 = 104.15 degrees...

now for the other diagonal....

the shorter diagonal will bisect the 104.15 degree angle
so if a perpendicular to the 10 units side is drawn a triangle is formed between the perpendicular the 15 unit side and the part of the ten unit side with an angle of 104.15/2 = 52.075 degrees bet 10 and 15 units side

now sine 52.075 = 8.727 (the height) / shorter diagonal

therefore the shorter diagonal is 11.06

Answer 3

AHEM!!! In case you slept through that portion of the class, the diagonals of a paralleogram are equal to each other. Use the law of cosines to compute the Cosine of one angle, and thence the angle. The other angle is its supplement.