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seropon [69]
3 years ago
7

Based on △GHI below, which of the following inequalities is true?

Mathematics
1 answer:
Rom4ik [11]3 years ago
4 0

Answer:

C. \overline{GI} < \overline{GH} < \overline{HI}

Step-by-step explanation:

In a triangle, the longest side is opposite to the largest measure of angle. The medium side is opposite to the medium angle, while the shortest side is opposite to the smallest angle.

In ∆GHI,

✍️m<G = 95°, it is opposite to \overline{HI}

<G is the largest angle, therefore, \overline{HI} is the longest side.

✍️m<I = 180 - (95 + 38) = 47°.

<I is opposite to \overline{GH}

<I is the medium angle, therefore, \overline{GH} is the medium side.

✍️m<H = 38°, it is opposite to \overline{GI}

<h is the smallest angle, therefore, \overline{GI} is the shortest side.

✅This means:

\overline{GI} < \overline{GH} < \overline{HI}

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Consider a triangle ABC for which ∠A=100∘,a=34,b=13. If such a triangle can not exist, then write NONE in each answer box. If th
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B is 22.12 degrees; ∠C is 57.88°; c=29.24

Step-by-step explanation:

So, first, it's important to draw a diagram of the triangle the problem is talking about (see  attached picture).

Once the triangle has been drawn, we can visualize it better and determine what to do. So first, we are going to find what the value of angle B is by using law of sines:

\frac{sin B}{b}=\frac{sin A}{a}

which can be solved for angle B:

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Once we know what the angle of B is, we can now find the value of angle C by using the fact that the sum of the angles of any triangle is equal to 180°. So:

A+B+C=180°

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c=sin C \frac{a}{sin A}

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