Question

The sides of a parallelogram are 20 feet and 40 feet long, and the smaller angle has a measure of 60°. Find the length of the longer diagonal to the nearest whole number.

Answer 1

Answer:

Length of the longer diagonal is 53 feet.

Step-by-step explanation:

We are given that,

Dimensions of the parallelogram is 40 feet and 20 feet and the smaller angle is 60°.

Let, the length of the diagonal be 'x' feet.

As the smaller angle is 60°, then the larger angle will be $\frac{360-2(60)}{2}$ = $\frac{360-120}{2}$ = $\frac{240}{2}$ = 120°

Using the Law of Cosines for the triangle made by the diagonal, we have,

$x^{2}=20^{2}+40^{2}-2\times 20\times 40\times \cos120$

i.e. $x^{2}=400+1600-1600\times (-0.5)$

i.e. $x^{2}=2000+800$

i.e. $x^{2}=2800$

i.e. x= 53 feet

Thus, the length of the longer diagonal is 53 feet.

Answer 2

Answer:

53 ft

Step-by-step explanation: