Question

In a ∆ABC, if ∠C = 60°, a = 47 cm and b = 94 cm, then c² = ____________.

Answer 1

Given ∠C = 60^∘ , a = 47 , b = 94 In ∆ABC

Using cosC = $\frac{a^2+b^2-c^2}{2ab}$

i.e cos 60^∘ = $\frac{{\left(47\right)}^2+{\left(94\right)}^2-C^2}{2\times 47\times 94}$

i.e $2\times \frac{1}{2}\times 47\times 94={\left(47\right)}^2+{\left(94\right)}^2-C^2$

i.e C² = (47)² + (94)² − 47 × 47 × 2
= − (47)² + (94)²
∴ C² = 8836 − 22049 = 6627