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rusak2 [61]
3 years ago
14

Find side lengths C and H

Mathematics
1 answer:
Nuetrik [128]3 years ago
3 0

Answer:

\displaystyle c=\frac{2\sqrt{3}}{3}\\\\\displaystyle h=7\sqrt{2}\\

Step-by-step explanation:

<u>Right Triangles</u>

A right triangle can be identified by the fact it has an internal angle of 90°. In a right triangle, the trigonometric ratios stand.

Let's consider the triangle to the left.  We need to calculate side c, one of the legs of the triangle. We can use the angle adjacent to it (60°) or the angle opposite to it (30°) with the appropriate trigonometric ratio.

We'll use the adjacent angle, and

\displaystyle tan60^o=\frac{2}{c}

Solving for c

\displaystyle c=\frac{2}{tan60^o}=\frac{2}{\sqrt{3}}

Rationalizing

\displaystyle c=\frac{2}{\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}

Now for the triangle to the right. The side h is the hypotenuse. Again, any of the two angles can be used (though they are equal, for it's an isosceles triangle). For any of them it is true that

\displaystyle sin45^o=\frac{7}{h}

Solving for h

\displaystyle h=\frac{7}{sin45^o}=\frac{7}{\frac{\sqrt{2}}{2}}=\frac{14}{\sqrt{2}}

Rationalizing

\displaystyle h=\frac{14}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{14\sqrt{2}}{2}=7\sqrt{2}

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Answer:

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Step-by-step explanation:

This is because there are 14 yellow marbles, and 6 red marbles. Along with this, half of the red marbles are made out of plastic. This leaves 3/6 of the red marbles made out of plastic. When combined with the yellow marbles, you'll add 14 to the denominator, since there are 14 yellow marbles. (Red + Yellow = Total Number Of Marbles) This leads to a total count of 3 marbles of the 20 total marbles, being red and made out of plastic.

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A _____ is accepted to be true without proof, while a _____ is an assertion that can be proven using the rules of logic.
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Answer:

A <u>postulate</u> is accepted to be true without proof, while a <u>theorem </u>is an assertion that can be proven using the rules of logic.

Explanation:

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Read 2 more answers
Please answer now I’m giving out 100 points
N76 [4]

4 liters of punch can serve 16.

5 liters of punch will be needed for 20 servings.

7 liters of punch will serve 28.

Step-by-step explanation:

Given,

Ratios of liters of punch to servings = 2:8

Let,

x be the servings for 4 liters.

New ratio of liters of punch to servings = 4:x

Using proportion;

Ratio :: New ratio

2:8::4:x

Product of mean = Product of extreme

8*4=2*x\\32=2x\\2x=32

Dividing both sides by 2

\frac{2x}{2}=\frac{32}{2}\\x=16

4 liters of punch can serve 16.

Let,

y be the liters of punch for 20 servings.

New ratio = y:20

Using proportion;

2:8::y:20

Product of mean = Product of extreme

8*y=20*2\\8y=40\\

Dividing both sides by 8

\frac{8y}{8}=\frac{40}{8}

y=5

5 liters of punch will be needed for 20 servings.

Let,

z be the number of servings for 7 liters of punch.

New ratio = 7:z

Using proportion

2:8::7:z\\

Product of mean = Product of extreme

8*7=2*z\\56=2z\\2z=56

Dividing both sides by 2

\frac{2z}{2}=\frac{56}{2}\\z=28

7 liters of punch will serve 28.

Keywords: ratio, proportion

Learn more about ratios at:

  • brainly.com/question/2154850
  • brainly.com/question/2367554

#LearnwithBrainly

4 0
3 years ago
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