Question

Given ∆ABC, m∠A=120°,b=13 cm,c=15 cm. Find the length of side a. Draw the triangle and label it. Show all work to find the missing side length. Use appropriate units.

Answer 1

Answer:

$24.269\ \text{cm}$

Step-by-step explanation:

$m\angle A=120^{\circ}$

$b=13\ \text{cm}$

$c=15\ \text{cm}$

From the law of cosines we know that

$a^2=b^2+c^2-2bc\cos A\\\Rightarrow a=\sqrt{b^2+c^2-2bc\cos A}\\\Rightarrow a=\sqrt{13^2+15^2-2\times 13\times 15\cos120^{\circ}}\\\Rightarrow a=24.269\ \text{cm}$

The side $a$ of the triangle is $24.269\ \text{cm}$.