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NeX [460]
3 years ago
8

the coordinates of the vertices of triangle ABC are a (-2,2), b (5,-3), c (-4,-1). Identify the perimeter of triangle ABC.

Mathematics
1 answer:
Natali5045456 [20]3 years ago
8 0

The formula of a distance between two points:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

A(-2,\ 2);\ B(5,\ -3)\\\\AB=\sqrt{(5-(-2))^2+(-3-2)^2}=\sqrt{49+25}=\sqrt{74}\\\\A(-2,\ 2);\ C(-4,\ -1)\\\\AC=\sqrt{(-4-(-2))^2+(-1-2)^2}=\sqrt{4+9}=\sqrt{13}\\\\B(5,\ -3);\ C(-4,\ -1)\\BC=\sqrt{(-4-5)^2+(-1-(-3))^2}=\sqrt{81+4}=\sqrt{85}\\\\P_{\triangle ABC}=\sqrt{74}+\sqrt{13}+\sqrt{85}

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Truth statement are statements or assertions that is true regardless of whether the constituent premises are true or false. See below for the definition of Euclidean Postulates.

<h3>What are the Euclidean Postulates?</h3>

The five Euclidean Postulates are;

1. Any two points can be joined by a straight line segment.

2. In a straight line, any straight line segment can be stretched indefinitely.

3. A circle can be formed using any straight line segment as the radius and one endpoint as the center.

4. Right angles are all the same.

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Read more about Euclidean postulate at; brainly.com/question/17304015

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8 0
2 years ago
Which equations for the measures of the unknown
MAXImum [283]

Answer: Option B, Option C, Option E

Step-by-step explanation:

The options written correctly, are:

A)x = cos^{-1}(\frac{a}{c})\\\\B) x = sin^{-1}(\frac{c}{b})\\\\C)x = tan^{-1}(\frac{c}{a})\\\\D) y = sin^{-1}(\frac{a}{c})\\\\ E)y = cos^{-1}(\frac{c}{b})

For this exercise you need to use the following Inverse Trigonometric Functions:

1)\ sin^{-1}(x)\\\\2)\ cos^{-1}(x)\\\\3)\ tan^{-1}(x)\\\\

When  you have a Right triangle (a triangle that has an angle that measures 90 degrees) and you know that lenght of two sides, you can use the Inverse Trigonometric Functions to  find the measure of an angle \alpha:

 1)\alpha = sin^{-1}(\frac{opposite}{hypotenuse}) \\\\2)\ \alpha =cos^{-1}(\frac{adjacent}{hypotenuse})\\\\3)\ \alpha=tan^{-1}(\frac{opposite}{adjacent})

Therefore, the conclusion is that the angles "x" and "y" can be found with these equations:

x=sin^{-1}(\frac{c}{b})\\\\x= cos^{-1}(\frac{a}{b})\\\\x=tan^{-1}(\frac{c}{a})\\\\\\ y=sin^{-1}(\frac{a}{b})\\\\y=cos^{-1}(\frac{c}{b})\\\\y=tan^{-1}(\frac{a}{c})

5 0
3 years ago
Read 2 more answers
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