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4 years ago

What is the value of x?

Mathematics

1 answer:

Alex787 [66]4 years ago

5 0

Answer:

Step-by-step explanation:

SOH CAH TOA reminds you that ...

Sin = Opposite/Hypotenuse

so ...

sin(45°) = (6√2)/x

Your memory of trig functions tells you sin(45°) = 1/√2, so we have ...

1/√2 = (6√2)/x

Multiplying by (√2)x gives ...

x = 6(√2)^2 = 6·2

x = 12

_____

You can simply recognize that this is an isosceles right triangle, so the hypotenuse (x) is √2 times the leg length:

x = (6√2)·√2 = 6·2 = 12

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if the following line are parallel peroendicular coinciding or intersectining but not perpendicular ????

Lapatulllka [165]

Answer:In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects. A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles.

Step-by-step explanation:

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3 years ago

Find the values of x and y. Round your answers to the nearest tenth if necessary,

Eduardwww [97]

Answer:

$x=12,\\y=12\sqrt{3}$

Step-by-step explanation:

In any 30-60-90 triangle, the side lengths are in the ratio $x:x\sqrt{3}:2x$ , where $2x$ is the hypotenuse, or longest side, of the triangle and $x$ is the side opposite to the 30 degree angle.

In the given 30-60-90 triangle, the longest side (hypotenuse) is marked as 24. Since $x$ is opposite to the 30 degree angle,

Therefore, we have:

$x=\frac{24}{2},\\x=\boxed{12}$

Based on our side length ratio $x:x\sqrt{3}:2x$ , $y$ is then:

$y=x\sqrt{3}\text{ for}\implies x=12,\\y=\boxed{12\sqrt{3}}$

5 0

4 years ago

Read 2 more answers

(-2, 1), (-1, 4), (0, 4), (1, 6), (2, 7) <br><br> find domain and range

IgorC [24]

Answer:

(-2,-1,0,1,2)

(1,4,6,7)

6 0

2 years ago

The sum of the diagonals of a rhombus is 5√2.

Alex

Greetings!
Let ABCD be a rhombus
AC + BD = 5√2 cm

Area of ABCD = Ar△ABD + Ar △BCD
$= \frac{1}{2} \times BD \times AO + \frac{1}{2} \times BD \times OC$
$= \frac{1}{2} BD (AO + OC)$
$\frac{1}{2} BD \times AC$

$So, \frac{ BD \times AC}{2} = 4 \: cm {}^{2}$
$BD \times AC = 8$
$Now, AC + \: BD = 5 \sqrt{2}$

Squaring both sides, we get
$AC {}^{2} + BD {}^{2} + 2 AC.BD =50$
$AC {}^{2} + BD {}^{2} + 2 \times 8 = 50$
$AC {}^{2} + BD {}^{2} = 50 - 16$
$AC {}^{2} + BD {}^{2} = 34$

In △AOB, we have
$OA {}^{2} + OB {}^{2} =AB {}^{2}$
$( \frac{ AC }{2} ) {}^{2} + ( \frac{ BD}{2} ) {}^{2} = AB {}^{2}$
$\frac{ AC {}^{2} } {4} + \frac{ BD {}^{2} }{4} = AB {}^{2}$
$AC {}^{2} + BD {}^{2} = 4 AB {}^{2}$
$34 = 4 AB {}^{2}$

Square rooting both sides
$\sqrt{34} = 2 AB$
$Perimeter = 4 \: AB \\ = 2 \times 2 \: AB \\ = 2 \: \times \sqrt{34 } \\ = 2 \sqrt{34 \: } units$ .

Hope it helps!

7 0

4 years ago

What percent of 90 is 54?

Helga [31]

Answer should be 60! hope this helps :)

5 0

4 years ago

Read 2 more answers