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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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Dmitriy789 [7]

1 liter of petrol in London costs £1.029

Since 1 gallon consist of 3.7854 liters, the cost of 3.7854 liters is calculated as:

Cost of 1 gallon of petrol in London = 3.7854*1.029 =£3.8951766

Next, we convert the pounds (£) to dollar($)

Since the exchange rate is 1$ =£ 0.497

£3.8951766 in $ = £3.8951766/£ 0.497 = 7.837$

The price of London petrol in dollars ($) per gallon =$7.84 (Rounded to nearest cents)


3 0
2 years ago
A car salesperson received a commission of $2100 for a sale of $30,000. What was the rate of commission?
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3 years ago
Write this expression so that its denominator, if any, is a positive integer.<br> 2/(3+sqrt(7))
Tanzania [10]

Answer:

The Answer is 3 - sqrt7

Step-by-step explanation:

2/3 + sqrt7   the starting equation

You multiply it by the conjugate which is 3 - sqrt7

= 2(3 - sqrt7) / (3 + sqrt7) (3 - sqrt7)  the equation after you multiply by 3 - sqrt7

(3 + sqrt7) (3 - sqrt7) = 2

= 2(3 - sqrt7) / 2    the equation after you simplify (3 + sqrt7) (3 - sqrt7)

Divide out the 2's

= 3 - sqrt7/1    the equation after you divide out the 2's

= 3 - sqrt7  is THE ANSWER

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Which ordered pair is a solution to the system of inequalities?<br> y&gt;−2 and x+y≤4
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Step-by-step explanation:

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Here is the work for that problem

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