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goblinko [34]
3 years ago
10

Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which t

wo numbers the length of the third side must fall.) Write an inequality.
8 and 13
Mathematics
1 answer:
Sidana [21]3 years ago
3 0
<h3>Answer:  5 < x < 21</h3>

Explanation:

Let x be the length of the third side. We can't find the exact value of x, as we don't have enough info, but we can find possible values for x.

The lower boundary for x is 13-8 = 5. It must be larger than this value.

At the same time, x must be smaller than 13+8 = 21 as well.

So x > 5 and x < 21 becomes 5 < x < 21

In short, x is between 5 and 21. It cannot equal either endpoint.

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Answer:

10. Not enough information

11. B ≈ 12.0°

12. A ≈ 34.1°

Step-by-step explanation:

10. Not enough information

11.

We need to use the Law of Sines, which states that for a triangle with lengths a, b, and c and angles A, B, and C:

\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}

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\frac{b}{sinB} =\frac{c}{sinC}

\frac{10}{sinB} =\frac{38}{sin128}

Solve for B:

B ≈ 12.0°

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Use the Law of Sines as above.

\frac{a}{sinA} =\frac{b}{sinB}

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Solve for A:

A ≈ 34.1°

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