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?

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

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boffeemadrid boffeemadrid · Answer 2 · 2019-03-19T11:35:20+01:00

Answer:

3.6

Step-by-step explanation:

It is given that a triangle has two sides of length 3 and 4 and that the angle between these two sides is [tex]\frac{\pi}{3}[/tex], thus using the cosine angle theorem, we have

[tex]c^2=a^2+b^2-2abcosC[/tex]

Substituting the given values, we get

[tex]c^2=4^2+3^2-2(4)(3)cos60^{\circ}[/tex]

[tex]c^2=16+9-24{\times}\frac{1}{2}[/tex]

[tex]c^2=16+9-12[/tex]

[tex]c^2=13[/tex]

[tex]c=3.6[/tex]

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