Question-97460

Question Number 97460 by mathocean1 last updated on 08/Jun/20

Commented by mathocean1 last updated on 08/Jun/20

A B + B C + A C = \dots ?

Commented by MJS last updated on 08/Jun/20

simply apply law of cosines

a = 400 b = 300 β = 105 °

b^{2} = a^{2} + c^{2} - 2 a c \cos β

Answered by smridha last updated on 08/Jun/20

A \vec{C} = B \vec{C} - A \vec{B}

∣ A C ∣= \sqrt{{(300)}^{2} + {(400)}^{2} - 2 (300) (400) c o s (105^{°})}

= 558.673 m

A B + B C + A C = 300 + 400 + 558.673

= 1258.673 m

Commented by 1549442205 last updated on 08/Jun/20

\cos 105 ° = - \sin 15 ° = - \sqrt{\frac{1 - \cos 30 °}{2}} =

- \sqrt{\frac{2 - \sqrt{3}}{4}} = - \frac{\sqrt{3} - 1}{2 \sqrt{2}} = \frac{- (\sqrt{6} - \sqrt{2})}{4}