Question

In the triangle ABC, if side a is 3, side b is 4 and side c is 5, what is the cosine of the smallest angle?

Answer 1

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.

$3^2+4^2=9+16=25$

Sum of squares of largest sides.

$5^2=25$

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.

$\cos \theta = \dfrac{adjacent}{hypotenuse}$

$\cos (A) = \dfrac{AC}{AB}$

$\cos (A) = \dfrac{4}{5}$

Therefore, the cosine of the smallest angle is 4/5.