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2 years ago

Find the distance from A(-8,-3,-2) and B(-4,8,0) , find ||AB||

Mathematics

1 answer:

RUDIKE [14]2 years ago

3 0

Answer:

$||AB|| = 11.8743$

Step-by-step explanation:

Distance between two points:

Suppose that we have two points, $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ . The distance between them is given by:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$

Distance from A(-8,-3,-2) and B(-4,8,0)

$||AB|| = \sqrt{(-4-(-8))^2+(8-(-3))^2+(0-(-2))^2}$

$||AB|| = \sqrt{4^2 + 11^2 + 2^2}$

$||AB|| = 11.8743$

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Step-by-step explanation:

We need to choose Pythagoras theorem formula

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$4225=4225$

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option-D:

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3 0

2 years ago

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Find the length of side x in simplest radical form with a rational denominator

Angelina_Jolie [31]

Answer:

The length of x=3/1

Step-by-step explanation:

Given the right triangle

Ф = 30

We know that

sin Ф = opposite/hypotenuse

The opposite of angle 30° = x

The hypotenuse is = 6

sin 30 = opposite/hypotenuse

1/2 = x/6 ∵ sin 30 = 1/2

1/2 × 6 = x

6/2 = x

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2 years ago

Find UV (Pic Stated Below)

natta225 [31]

Answer:

UV=29

Step-by-step explanation:

In right triangles AQB and AVB,

∠AQB = ∠AVB ...(i) {Right angles}

∠QBA = ∠VBA ...(ii) {Given that they are equal}

We know that sum of all three angles in a triangle is equal to 180 degree. So wee can write sum equation for each triangle

∠AQB+∠QBA+∠BAQ=180 ...(iii)

∠AVB+∠VBA+∠BAV=180 ...(iv)

using (iii) and (iv)

∠AQB+∠QBA+∠BAQ=∠AVB+∠VBA+∠BAV

∠AVB+∠VBA+∠BAQ=∠AVB+∠VBA+∠BAV (using (i) and (ii))

∠BAQ=∠BAV...(v)

Now consider triangles AQB and AVB;

∠BAQ=∠BAV {from (v)}

∠QBA = ∠VBA {from (ii)}

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So using ASA, triangles AQB and AVB are congruent.

We know that corresponding sides of congruent triangles are equal.

Hence

AQ=AV

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9-1=7x-5x

8=2x

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4=x

Now plug value of x=4 into UV=7x+1

UV=7*4+1=28+1=29

<u>Hence UV=29 is final answer.</u>

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