Answer to Question #151065 in Trigonometry for Angelo

Question

Find side a in ∆ABC, side b = 12 m, side c = 20 m and angle B = 45˚.

Answer 1

We know that cosine law states that,

$a=\sqrt{b^2+c^2-2bc\cos\theta}$

and we have,

$b=12m$

$c=20m$

$\theta=45\degree$

$a=\sqrt{12^2+20^2-2\times 12 \times 20 \times \cos45\degree}$

$a=\sqrt{144+400-480 \times \frac{\sqrt2}{2}}$

$a=\sqrt{544 - 240\sqrt2}$

$a\approx 14.3$