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Sergeu [11.5K]
4 years ago
12

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Mathematics
1 answer:
butalik [34]4 years ago
8 0
Where's the question?
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Find side lengths C and H
Nuetrik [128]

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}

3 0
4 years ago
10 and two thirds plus 2h is less than or equal to 4 and one third. What is h?
jok3333 [9.3K]
I think your answer is -3 and one sixth. im not too good at this, so i am so VERY sorry if this is wrong!
5 0
3 years ago
Hi! Im stuck on this question (Its attatched) and I dont know how to answer it.
Ksju [112]

Answer: The answer is 51.8 degrees or rounded it is 52 degrees.

Step-by-step explanation: The first side is 39 degrees, you add 39+2x+1+3x+13 = 180

39+1+13 = 53

5x=127

x=25.4

2(25.4) + 1 = 51.8

4 0
3 years ago
Which number is greatest?<br> 6.23 x 10^12<br> O 6.23 x 10^8<br> 6.23 x 10^-6<br> 6.23 x 10^3
kaheart [24]

Answer:

The first one is greatest.

Step-by-step explanation:

4 0
3 years ago
An x-method chart shows the product a c at the top of x and b at the bottom of x. Below the chart is the expression a x squared
Zina [86]

Answer:

The pair of numbers that has a product of ac and a sum of b = (+2, +8)

The factored form of the trinomial = (x+2) (x+8)

Step-by-step explanation:

ax² + bx + c = 0

This is in the form of a trinomial algebraic expression

Given trinomial: = ax² + 10x + 16

Where a = 1, b= 10, c= 16

To find the pair of numbers that has a product of ac and a sum of b, we would solve the equation.

Using factorisation method:

ac = a×c = 1×16 = 16

Let's find the factors of 16 whose sum gives +10 and product gives +16

Factors of 16 = 1, 2, 8, 16

+2 + +8 = +10

+2 × +8 = +16

The factors are +2 and +8

The pair of numbers that has a product of ac and a sum of b = (+2, +8)

x² + 10x + 16 = x + 2x + 8x + 16

x² + 10x + 16 = x(x+2) + 8(x+2)

= (x+2) (x+8)

The factored form of the trinomial = (x+2) (x+8)

9 0
3 years ago
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