Suppose a triangle has two sides of length 3and 4 and that the angle between these two sides is 60. What is the length of the third side of the triangle?

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  A.  √13

Step-by-step explanation:

You can make an educated guess and come to the right conclusion.

The triangle is nearly an equilateral triangle. A triangle with two sides 3 and an angle of 60° would have a third side of 3. A triangle with two sides of 4 and an angle of 60° would have a third side of 4.

So, the third side must be between 3 and 4. Here is an evaluation of the answer choices:

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A -- between 3 and 4, the correct choice

B -- 3, too short

C -- 1.73, too short

D -- more than 4, too long

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The question can be answered using your triangle solver app on your calculator, or using the Law of Cosines.

  c = √(a^2 +b^2 -2ab·cos(C))

  c = √(3^2 +4^2 -2·3·4·(1/2)) = √(9 +16 -12)

  c = √13 . . . . . length of the side opposite the 60° angle

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right