the perimeter of a triangle is 60 cm one of its sides is 23 cm another is 24 cm calculate the size of the smallest angle in this triangle gi

The remaining side = 13cm

And the smallest angle will be opposite this side....so ....using the Law of Cosines  and the cosine inverse, we have

cos^-1  ((13^2 - 24^2 -23^2) / ((-2)(24)(23) )  = Θ  = about 32.0°

Hello anonymous!

a = 23 cm; b = 24 cm ; P = 60 cm

c = P - b - a = (60 - 24 - 23) cm = 13 cm

c² = a² + b² - 2ab * cos γ

2ab * cosγ = a² + b² - c² 

cos γ = (a² + b² - c²) / 2ab

cos γ = (23² + 24² - 13²) cm² / 2 * 23 * 24 cm²

cos γ = 0,847826086958

γ = arc cos 0,847826086958

γ = 32,024°  

The smallest angle in this triangle is γ = 32,024°

With regards, asinus  :- )