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luda_lava [24]
3 years ago
15

What is the value of x?

Mathematics
1 answer:
soldi70 [24.7K]3 years ago
3 0

Answer:

5\sqrt{3}

Step-by-step explanation:

A triangle with angles of 30-60-90 will always have sides that measure in the following proportions:

The side opposite the 30* angle = a

The side opposite the 60* angle = a\sqrt{3}

The side opposite the 90* angle = 2a

(I used "a" here because your question uses "x" and I don't want to confuse things, but usually people use "x" rather than "a")

They gave us that the hypotenuse (the side opposite the 90* angle) is 10, from there we can figure out the other sides:

Since the side opposite 90* is 2a, and 2a = 10, divide 10 by 2 and you get a = 5.

Once we know what "a" is, we can fill in the rest:

30* = 5

60* = 5\sqrt{3}

90* = 10

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Find the perimeter of the polygon with the vertices X(−1, 3), Y(3, 0), and Z(−1,−2). Round your answer to the nearest hundredth
antoniya [11.8K]

Answer:

The perimeter of the polygon is P=14.47\ units

Step-by-step explanation:

we know that

The perimeter is the sum of the length sides of the polygon

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P=XY+YZ+XZ

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

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X(−1, 3), Y(3, 0)

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step 2

Find the distance YZ

we have

Y(3, 0), Z(−1,−2)

substitute

d=\sqrt{(-2-0)^{2}+(-1-3)^{2}}

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step 3

Find the distance XZ

we have

X(−1, 3), Z(−1,−2)

substitute

d=\sqrt{(-2-3)^{2}+(-1+1)^{2}}

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step 4

Find the perimeter

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P=5+4.47+5=14.47\ units

5 0
3 years ago
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