Question

8. In AABC, AB = 6 cm, BC = 8 cm and ZABC =
150°. Find the area of AABC.
A
6 cm
150°
-С
8 cm
B
[Hint: Drop AP I CB extended.]​

Answer 1

Answer:

$ac = \sqrt({6} c m {)}^{2} + (8cm {)}^{2} \\ \sqrt({3} 6 + 64)c {m} ^{2} \\ \sqrt{1} 00c {m}^{2} \\ = 10cm$

AC = 10 cm, BC = 8 cm & AB = 6cm

semiperimeter = 24 / 2 = 12 cm

heron's formula

$\sqrt{1} 2 \times 12 - 6 \times 12 - 8 \times 12 - 10 \\ \sqrt{1} 2 \times 6 \times 4 \times 2 \\ \sqrt{2} \times 2 \times 3 \times 2 \times 3 \times 2 \times 2 \times 2 \\ = (2 \times 2 \times 2 \times 3 )c {m}^{2} \\ = 24c {m}^{2}$

Area = 24 cm square