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Reptile [31]
3 years ago
6

Which angle measures approximately 57°

Mathematics
1 answer:
blagie [28]3 years ago
4 0
An acute angle seems fit, 0° to 90<span>° are usually classified as acute triangles.</span>
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On a coordinate plane, triangle A B C is shown. Point A is at (0, 0), point B is at (3, 4), and point C is at (3, 2). What is th
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Answer:

The area of triangle for the given coordinates is  1.5\sqrt{4.6}

Step-by-step explanation:

Given coordinates of triangles as

A = (0,0)

B = (3,4)

C = (3,2)

So, The measure of length AB = a = \sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}

Or, a = \sqrt{(3-0)^{2}+(4-0)^{2}}

Or, a =  \sqrt{9+16}

Or, a =   \sqrt{25}

∴ a = 5 unit

Similarly

The measure of length BC = b = \sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}

Or, b = \sqrt{(3-3)^{2}+(2-4)^{2}}

Or, a =  \sqrt{0+4}

Or, b =   \sqrt{4}

∴ b = 2 unit

And

So, The measure of length CA = c = \sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}

Or, c = \sqrt{(3-0)^{2}+(2-0)^{2}}

Or, c =  \sqrt{9+4}

Or, c =   \sqrt{13}

∴ c = \sqrt{13} unit

Now, area of Triangle written as , from Heron's formula

A = \sqrt{s\times (s-a)\times (s-b)\times (s-c)}

and s = \frac{a+b+c}{2}

I.e  s = \frac{5+2+\sqrt{13}}{2}

Or. s =  \frac{7+\sqrt{13}}{2}

So, A = \sqrt{(\frac{(7+\sqrt{13})}{2})\times ((\frac{(7+\sqrt{13})}{2})-5)\times (\frac{7+\sqrt{13}}{2}-2)\times (\frac{7+\sqrt{13}}{2}-\sqrt{13})}

Or, A = \sqrt{(\frac{(7+\sqrt{13})}{2})\times (\frac{(\sqrt{13}-3)}{2})\times (\frac{4+\sqrt{13}}{2})\times (\frac{7-\sqrt{13}}{2})}

Or, A = \frac{3}{2} × \sqrt{1+\sqrt{13} }

∴  Area of triangle = 1.5\sqrt{4.6}

Hence The area of triangle for the given coordinates is  1.5\sqrt{4.6}  Answer

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3 years ago
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What Are the factors of 24 and 32
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Answer:

The factors of 24 are 24, 12, 8, 6, 4, 3, 2, 1

The factors of 32 are 32, 16, 8, 4, 2, 1.

Step-by-step explanation:

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The angle of depression from a lighthouse to a boat in the water is 14 degrees. If the boat is 532 feet from the base of the lig
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Step-by-step explanation:

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Which fraction is equal to 30%
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Answer:

Step-by-step explanation:

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Suppose p = (1, 3, 4) and q = (5, 8, 12) are solutions to the linear system of equations: a11x1 + a12x2 + a13x3 = α1 a21x1 + a22
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Answer:

Let A=\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\\a_{41}&a_{42}&a_{43}\end{array}\right] the matrix associated to the system and

b=\left[\begin{array}{ccc}\alpha_{1}\\\alpha_{2}\\\alpha_{3}\\\alpha_4\end{array}\right] the vector of constant values of the system.

The equation of the line joining p and q is

p+t(q-p), t\in\mathbb{R}. Since p and q are solutions of the linear system then, Ap=b and Aq=b

Let w=q-p. Observe that Aw=A(q-p)=Aq-Ap=b-b=0. Then w is a solution of the homogeneous system Ax=0.

Now, let s=p+r(q-p) for some r\in\mathbb{R}  be a point in the line joining p and q. Observe that

As=A(p+r(q-p))=Ap+rA(q-p)=Ap+rAw=b+r*0=b

Then As=b. This means that s is a solution of the linear system.

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