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3 years ago

The endpoints of EF are E(1,3) and F(-2,8). Find EF.

Mathematics

1 answer:

Phantasy [73]3 years ago

8 0

Answer:

EF = $\sqrt{34}$ ≈ 5.83

Step-by-step explanation:

Calculate EF using the distance formula

d = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = E(1, 3) and (x₂, y₂ ) = F(- 2, 8)

EF = $\sqrt{(-2-1)^2+(8-3)^2}$

= $\sqrt{(-3)^2+5^2}$

= $\sqrt{9+25}$

= $\sqrt{34}$ ≈ 5.83 ( to 2 dec. places )

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2 years ago

I need to know the improper fractions answers for:

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Part 1) $x=\frac{15}{2}\ units$

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Part 3) $y= \frac{15\sqrt{3}}{4}\ units$

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Step-by-step explanation:

step 1

Find the value of x

In the large right triangle

$cos(60^o)=\frac{x}{15}$ ----> by CAH (adjacent side divided by the hypotenuse)

Remember that

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step 2

Find the value of z

In the large right triangle

Applying the Pythagorean Theorem

$15^2=x^2+z^2$

substitute the value of x

$15^2=(\frac{15}{2})^2+z^2$

solve for z

$z^2=15^2-(\frac{15}{2})^2$

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$z=\frac{\sqrt{675}}{2}\ units$

simplify

$z=\frac{15\sqrt{3}}{2}\ units$

step 3

Find the value of y

In the right triangle of the right

$sin(30^o)=\frac{y}{z}$ ---> by SOH (opposite side divided by the hypotenuse)

substitute the given values of y and z

Remember that

$sin(30^o)=\frac{1}{2}$

$\frac{1}{2}=y:\frac{15\sqrt{3}}{2}$

solve for y

$\frac{1}{2}= \frac{2y}{15\sqrt{3}}$

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step 4

Find the value of b

In the right triangle of the right

$cos(30^o)=\frac{b}{z}$ ---> by CAH (adjacent side divided by the hypotenuse)

substitute the given values of y and z

Remember that

$cos(30^o)=\frac{\sqrt{3}}{2}$

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solve for y

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$b= \frac{45}{4}\ units$

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