Question

ABCD is a parallelogram . If AB is 8 cm long , BC is 5 cm and their included angle measure 100°, how long is diagonal AC?

Answer 1

Answer: 10.1436 cm

Step-by-step explanation:

By the cosine law,

$AC^2 = AB^2 + BC^2 - 2\times AB\times BC\times cos 100^{\circ}$

Given, AB = 8 cm, BC = 5 cm,

And, $m\angle ABC = 100^{\circ}$

Hence,

$AC^2 = (8)^2 + (5)^2 - 2\times 8\times 5\times cos 100^{\circ}$

$AC^2 = 64 + 25 - 80\times cos 100^{\circ}$

$AC^2 = 89 + 13.8918542134\implies AC=10.1435622053\approx 10.1436$

Answer 2

Answer:

The length of diagonal AC is 4.5 cm

Step-by-step explanation:

Given ABCD is a parallelogram . If AB is 8 cm long , BC is 5 cm and their included angle measure 100°. We have to find the length of diagonal AC.

In ΔABC

By cosine formula,

$b^2=a^2+c^2-2accosB$

⇒ $AC^2=AB^2+BC^2-2(AB)(BC)cosB$

⇒ $AC^2=8^2+5^2-2(8)(5)cos100^{\circ}$

⇒ $AC^2=64+25-80(0.862)^{\circ}$

                =20.04

⇒ AC=4.4766~4.5