A parallelogram has sides of lengths 4 and 9, and one angle is 48°.

Question

What is the length of the smaller diagonal?

length =  ______ units

What is the length of the longer diagonal?

length =  ______ units

Answer 1

parallelogram with sides 4 and 9, with angles 48 and 180-48= 132 degrees

what are the diagonal lengths?

use the law of cosines

d^2 = 16+81-2(4)(9)cos48= shorter diagonal squared

= 97-72cos48

=48.82

d= about 6.99 = about 7

d^2 = 16+81-2(4)(9)cos132 = longer diagonal squared

=97-72cos132

d=about 12.05= about 12

about 7 and 12