Answer:
Cosine of the smallest angle is 4/5.
Step-by-step explanation:
It is given that in the triangle ABC, side a is 3, side b is 4 and side c is 5.
Sum of squares of two smaller sides.
[tex]3^2+4^2=9+16=25[/tex]
Sum of squares of largest sides.
[tex]5^2=25[/tex]
Since sum of squares of two smaller sides is equal to sum of squares of largest sides, therefore triangle ABC is a right angle triangle.
Hypotenuse = 5 units.
In a right angle triangle, the smallest angle has shortest opposite side.
Shortest side is a=3 It means angle A is smallest.
[tex]\cos \theta = \dfrac{adjacent}{hypotenuse}[/tex]
[tex]\cos (A) = \dfrac{AC}{AB}[/tex]
[tex]\cos (A) = \dfrac{4}{5}[/tex]
Therefore, the cosine of the smallest angle is 4/5.
