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3 years ago

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

Elena L [17]

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

Liula [17]

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:

8 0

3 years ago

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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

MA_775_DIABLO [31]

Answer:132.6tt

Step-by-step explanation:

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3 years ago

Which fraction is equal to 30%

Nookie1986 [14]

Answer:

Step-by-step explanation:

$\frac{30}{100}=\frac{3}{10}$

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4 years ago

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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

Alex73 [517]

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.

8 0

3 years ago