Respuesta :
a² = b² + c² – 2bccos(A)
The smallest angle is across the smallest side, so
4²=5²+6²-2*5*6*cos(Q)
16=25+36-60*cos(Q)
16-36-25=-60*cos(Q)
45=60*cos(Q)
cos(Q)=45/60
Q=cos⁻¹(45/60) ≈41⁰
The smallest angle is across the smallest side, so
4²=5²+6²-2*5*6*cos(Q)
16=25+36-60*cos(Q)
16-36-25=-60*cos(Q)
45=60*cos(Q)
cos(Q)=45/60
Q=cos⁻¹(45/60) ≈41⁰
Answer:The smallest angle of the triangle will be nearest to 41°.
Explanation:
since, the sides of the triangle are 4,5 and 6.
when we talk about the smallest angle then it must be the opposite angle of side 4.
Thus according to the law of cosines,
[tex]4^2=5^2+6^2-2\times5\times6\times cos(A)[/tex](where A(let) be the smallest angle of the triangle.)
⇒16=25+36-60cos(A)
⇒16-61=-60cos(A)
⇒-45=-60cos(A)
⇒[tex]cos(A)=3/4\implies A = cos^{-1}(3/4)[/tex] ⇒A=41.4096221093 degree [tex]\approx[/tex] 41°
