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

`24.269\ \text{cm}`

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=√(b^2+c^2-2bc\cos A)\\\Rightarrow a=\sqrt{13^2+15^2-2* 13* 15\cos120^(\circ)}\\\Rightarrow a=24.269\ \text{cm}`

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