Question

Suppose a triangle has two sides of length 3 and 4 and that the angle between these two sides is pi/3. What is the length of the third side of the triangle?

Answer 1

3.6

Explanation:

It is given that a triangle has two sides of length 3 and 4 and that the angle between these two sides is
`(\pi)/(3)`, thus using the cosine angle theorem, we have

`c^2=a^2+b^2-2abcosC`

Substituting the given values, we get

`c^2=4^2+3^2-2(4)(3)cos60^(\circ)`

`c^2=16+9-24{*}(1)/(2)`

`c^2=16+9-12`

`c^2=13`

`c=3.6`

Therefore, the length of the third side of the triangle will be 3.6

Answer 2

We can use the Cosine Law ( π / 3 = 60° ):
c² = a² + b² - 2 a b cos C
c² = 4² + 3² - 2 · 4 ·3 · cos 60° = 16 + 9 - 24 · 1/2 = 25 - 12 = 13
Answer:
The length of the third side of a triangle is c = √ 13 ≈ 3.6