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We're looking for an angle where the sine = (√3)/2

This happens at 60 degrees and at 120 degrees

A more general solution (in degrees) would be..... 60 + n360  and 120 +n360  where n is an integer

In radians, the general solution would be ... pi/3 + n(2pi)   and 2pi/3 + n(2pi)  where n is an integer

You can plug this into a calculator: $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\frac{{\sqrt{{\mathtt{3}}}}}{{\mathtt{2}}}}\right)} = {\mathtt{60^{\circ}}}$$

Or, you can use the unit circle (a circle with a radius of 1 which is very useful for finding exact values of angles with 30, 45, and 60 degree reference angles).

We have an angle and its adjacent side...we need to find the opposite side....the tangent function relates these three things

tan(38) = x/28    where x is the flagpole height  ..so...

28tan(38) = 21.88 m

You would use the tangent of the angle to find the height of the flagpole, h.

Tangent is opposite/adjacent, and in this problem the opposite side is the height of the pole (h) while the adjacent side is the length to the pole's base (28).

Therefore: 

tan(38) = opp/adj

tan(38) = h / 28

Multiply both sides by 28.

$${\mathtt{h}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{38}}^\circ\right)}{\mathtt{\,\times\,}}{\mathtt{28}} \Rightarrow {\mathtt{h}} = {\mathtt{21.875\: \!997\: \!542\: \!196}}$$

The flagpole is approximately 21.88 m tall.

You have to give us the numbers and the rules and then we can do it for you.

If they sell 100000 tickets and you buy one then your chance of winning is 1 in 100000.

11/6/14

A cute pic!

Thanks Ninja.

A great answer NinjaDevo.  

Uh... With a calculator?

5x-3=(x+7)+3

5x-3=x+10

-x      -x               ---Subtract x from both sides

4x-3 = 10

    +3   +3              ---Add 3 to both sides

4x = 13

/4      /4               ---Divide both sides by 4

x = 13/4

or

x = 3.25

Let's check it:

5(3.25)-3=((3.25)+7)+3

16.25-3 = 10.25 + 3

13.25 = 13.25

Let's set up an equation for this word problem, and let's make x equal the second number.

x+(x+17)=157     ---Since the first number is 17 bigger than the second number, (x+17) will give us the first   number.

2x + 17 = 157

     -17      -17

2x = 140

x = 70

So our second number is 70, and our first number is 87 (17 bigger than our second number, so 17+70)

Trust me its 0% all the time.....or maybe its just me

Dividing a number by a fraction is equivalent to multiplying that number by the fraction's reciprocal.

So sqrt(3) /2 divided by 1/2 is the same as sqrt(3) /2 multiplied by 2/1.

You can cross-cancel the 2s, since you are dividing by 2, then multiplying by 2.

= sqrt(3)/1

=$${\sqrt{{\mathtt{3}}}}$$

Hola,

NinjaDevo te ayudó con su sitios web, (thanks NinjaDevo:)

La tangente de un ángulo (x) en la trigonometría es: cateto opuesto (o) / cateto adyacente (a)

Entonces, la tangente de ángulo x es o / a

the answer is 87 + 70 x

5x-3=(x+7) +3x

5x-3 = 4x+7

-4x     -4x          ---Subtract 4x from both sides

x-3 = 7

+3   +3             ---Add three to both sides

x = 10

Let's check it:

5(10)-3=((10)+7) +3(10)

50-3 = 17+30

47 = 47

47 does equal 47; the statement is true, so we know this works.

Well, if this line is parallel to the line 2x+3y+7=0, that means it is the same as that line, but with a different y intercept

2x+3y+7=0

/3   /3  /3                    ---Divide everything by 3

2/3x + y + 7/3 = 0

-2/3x          -7/3               ---Subtract from both sides

y = -2/3x - 7/3

This is the same line in the slope-intercept form.

y = -2/3x + 6

I just changed the y intercept to 6, which is what we need. This is the first way we could write our answer. Or we could turn it back into the standard form of a line.

y = -2/3x + 6

      +2/3x

2/3x + y = 6

or

2x + 3y = 18

Hope this helps.

You took points off me because I took the time to try and help you.

Here I have given you considerable help and still you offer no thanks or gratitude of any kind.

You are one of the rudest people who has ever been on this forum.

Let other people decide how gracious you are!

(3.4x10¹²) ÷ (1.2x10^-3)

(3.4 ÷ 1.2) (10¹² ÷ 10^-3)

(2.833333)(10^12-(-3))

(2.833333)(10^12+(+3))

2.8333*10¹⁵

Round to 3 significant digits(or figures)

2.83*10¹⁵

And there you go!

kitty<3, answers questions in Spanish.

kitty<3, responde a las preguntas en español.

Bob has 1 crayon

 Selena has 5

We can add these together to find the answer, so

1+5 = 6 crayons

6 crayons

In order for us to subtract these, they need to have the same denominators, then we can subtract like we usually do.

$${\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{4}}}}$$                       

Now I can multiply both the top and bottom of the first fraction by 4, and the top and bottom of the second fraction by 3. We know this works because 8/12 is the same thing as 2/3 and 3/12 is the same thing as 1/4 

$${\frac{{\mathtt{8}}}{{\mathtt{12}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{3}}}{{\mathtt{12}}}}$$                   

$${\frac{{\mathtt{5}}}{{\mathtt{12}}}}$$           

Now I just subtracted to tops from each other. This can't be reduced, so 5/12 is our answer!

If this didn't make any sense at all, let me know and I can try to explain it differently!

It's not that obvious. For example,

$$a^{7}+b^{7}=(a+b)(a^{6}-a^{5}b+a^{4}b^{2}-a^{3}b^{3}+a^{2}b^{4}-ab^{5}+b^{6}).$$