please help its precalc homework

Question

A parallelogram has sides of lengths 7 and 8, and one angle is 43°.

What is the length of the smaller diagonal?

length =  units

What is the length of the longer diagonal?

length =  units

Answer 1

it this were 45 degrees between 7 and 8,

then the diagonals would be slightly less than 6 and 11

if it were nearly 0 degrees, then the diagonals would be nearly 1 and 15

if it were 90 degrees, the the diagonals would be equal and = about 11.63, the diagonal of a rectangle

with 43 degrees, the diagonals are about 5.6 and 14

it helps to draw a sketch

the smaller the angle, the closer to 15 is the longer diagonal and the closer to 1 is the shorter diagonal

use the law of cosines

d^2 = 7^2 + 8^2 -2(7)(8)cos43

= 49+64-112cos43

=113 -112(.7314)

=31.088

d =sqr31.088

d = 5.57 = shorter diagonal

if 43 is one angle between 7 and 8, the other angle is 180-43= 137

d^2= 113-112cos137

d^2= 113-112(-.7314)

d^2 = 194.9116

d=13.96 = the longer diagonal

diagonals are about 5.6 and 14

Answer 2

Draw and label a diagram

The smaller angle, 43°, is opposite the smaller diagonal.

Use Law of Cosines to determine length of smaller diagonal.