# Triangle has two sides that have lengths of 17 feet and 22 feet. Which ofthe following lengths could not represent the length of the third side?

length of the third side will have a value between 5 and 39.

Sol. 1)

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let

Given that

Hence, the third side

Sol.2)

Using the cosine law of solving triangles.

Let the included angle between sides

as

or

or

Hence, the third side

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According to the triangle inequality theorem, the length of the third side of a triangle must be less than the sum of the lengths of the other two sides and greater than their difference.

For a triangle with sides of 17 feet and 22 feet:

- The third side cannot be greater than 39 feet (17 + 22).
- The third side cannot be less than 5 feet (|17 - 22|).

So, any length less than 5 feet or greater than 39 feet could not represent the length of the third side.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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