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The angle between the tower and the hypotenuse is 180 - 90 - 30 = 60º

The angle between the hypotenuse of the right triangle and the flagpole is 180 - 60 = 120º.

The angle between the flagpole and the top line is 30º.

Use Law of Sines to find the hypotenuse of the right triangle.

\(\frac{5}{\sin30}=\frac{x}{\sin30} \\~\\ x = 5\)

Then you can find the height of the tower.

sin30 = tower/5

tower = 5sin30

tower = 2.5 m

I did this but I thought it was wrong because the tower was so short, but I'll go ahead and post it now because I drew a picture :)

Don't worry about it, JBDBIBBaerman.....we all make mistakes......we're just glad that you're participating......!!!

Just divide it by 100. Example: 25% =25/100 =0.25. And that is it!.

SORRY FOR DOUBLE POSTING!! IT GOT LOST THE FIRST TIME!!.

Wow! Messed up is right!.

This problem is quite involved for most students. However, with little bit of thinking, it turns out that it is no that complicated.

The first thing that the student has to keep in mind is that $50,000 that she saved in the first 15 years. You must bear in mind that it will continue to grow for another 15 years at the new rate of 5%. Therefore, if we project its FV for another 15 years @ 5% we will have =$103,946.41. Her total goal is to save $300,000. Therefore, the net amount she needs to save in the next 15 years is=$300,000 - $103,946.41 =$196,053.59.........(1)

Since she plans to double her deposits each and every year, will have to find the FV of $1, $2, $4, $8....and so on for 15 years @5%. We can easily do that on any good calculator, such as Wolfram/Alpha, such as I have done here:∑[(2^n * 1.05^(14-n)), n, 0, 14] =34,490.443233495......(2).

Now then, all we have to do is divide the amount in (1) above by (2) above and we get:

$196,053.59 / $34,490.44323495 =$5.68 - which would be her first payment for the remaining 15 years. And, of course, she will double that each and every year: $5.68 , $11.36, $22.72, $45.44...and so on. Here is the link to W/A:

http://www.wolframalpha.com/input/?i=%E2%88%91%5B(2%5En+*+1.05%5E(14-n)),+n,+0,+14%5D

I hope you understand what I have done. If you have any questions, just let me know here. Good luck.

Call the tower height,  P *tan(30)

And the  tower ht + the height of the flagstaff = P*tan(60)

And the difference between these two = the height of the flagstaff.....so

Ptan(60) - Ptan(30)  = 5

P [tan(60) - tan(30) ] = 5

P = 5 / [ tan (60) - tan(30) ]  = (5/2)sqrt(3)  m

So....the tower ht  = (5/2)sqrt(3)* tan(30)  =  2.5 m.....

Mmmmmm...not much of a tower !!!!

But....it's correct because the height of the tower and the flagstaff = (5/2)sqrt(3)* tan(60) =

7.5 m   !!!

Wow! Messed up is right!.

This problem is quite involved for most students. However, with little bit of thinking, it turns out that it is no that complicated.

The first thing that the student has to keep in mind is that $50,000 that she saved in the first 15 years. You must bear in mind that it will continue to grow for another 15 years at the new rate of 5%. Therefore, if we project its FV for another 15 years @ 5% we will have =$103,946.41. Her total goal is to save $300,000. Therefore, the net amount she needs to save in the next 15 years is=$300,000 - $103,946.41 =$196,053.59.........(1)

Since she plans to double her deposits each and every year, will have to find the FV of $1, $2, $4, $8....and so on for 15 years @5%. We can easily do that on any good calculator, such as Wolfram/Alpha, such as I have done here:∑[(2^n * 1.05^(14-n)), n, 0, 14] =34,490.443233495......(2).

Now then, all we have to do is divide the amount in (1) above by (2) above and we get:

$196,053.59 / $34,490.44323495 =$5.68 - which would be her first payment for the remaining 15 years. And, of course, she will double that each and every year: $5.68 , $11.36, $22.72, $45.44...and so on. Here is the link to W/A:

http://www.wolframalpha.com/input/?i=%E2%88%91%5B(2%5En+*+1.05%5E(14-n)),+n,+0,+14%5D

I hope you understand what I have done. If you have any questions, just let me know here. Good luck.

17-8=9

     x        80

7.00     100               x=$5.60

The polygons are not similar

AB/AD  =  7/2 / 3  = 2.4   but

KL/NK  = 5.4/1.8   = 3........and these would have to be the same for similarity

Perimeter

XZ = sqrt ( 5^2 + 3^2)  = sqrt (34)

XY = sqrt ( 4^2 + 5^2)  = sqrt (41)

YZ = sqrt ( 9^2 + 2^2)  = sqrt (85) 

sqrt (34) + sqrt(41) + sqrt (85) ≈  21.45  units.....correct  !!!

The area is a little difficult.....there are several ways to do this using trig.....but....I'm going to assume you might not have had that.....so....let's do this

The slope between Y(4,-4), and Z(-5,-2)  is (-2 - -4) / (-5 -4)  = 2/-9  = -2/9

And the equation of the line joining  these two points  is   y = (-2/9)(x - 4) - 4  →

y = (-2/9x + 8/9 - 4 →  y = (-2/9)x - 28/9

So...... a perpendicular line from the apex of the triangle - point X - to this line will serve as the height of the triangle.....and the slope of this perpendicular line will be the negative reciprocal of -2/9   = 9/2

And the equation of this line will be

y = (9/2) ( x - 0) + 1   → y =  (9/2)x + 1

Setting these lines equal, we can find the x coordinate of their intersection

(-2/9)x - 28/9   =  (9/2)x + 1

-28/9 - 1  =  (9/2 + 2/9)x

-37/9   = (85/18)x     multiply both sides by 18/85

(-37/9)(18/85)  =  -74/85

And the y coordinate of their intersection can be found  as  (9/2)(-74/85) + 1  = -248/85

So the distance from X -(0,1)- to  (-74/85, -248/85)  is given by

sqrt [ (74/85)^2 + ( 1 + 248/85)^2 ]  = 37/ sqrt (85)  = the triangle's  height

So.....the area of a triangle is (1/2) B * H  

The Base is YZ   = sqrt (85)....so the area =

(1/2)sqrt(85) * 37 / sqrt (85)   -  (1/2)(37)  = 18.5 square units  !!!

Whew!!!!....that was a lot of work......but....I verified the answer here :

http://www.wolframalpha.com/input/?i=area+triangle+%5B+(0,1),+(4,-4),++(-5,-2)%5D

Hope that helps !!!

20*21

FV = PV [1 + R]^N

100,000 = 67,000 x [1 + R]^15  divide both sides by 67,000

1.4925373.. = [1 + R]^15           take the 15th root of both sides

[1 + R] =1.027058...                   subtract 1 from both sides

R =0.027058 x 100

R =2.71%.

20x20=400

400+20=420

You can edit your answer, but I don't think you can delete it.

1 divided 1=1

1 divided by 1=1

Ignore me completely

Whoops. I'm not helpful here. I never answered before. That was definitely me being possesed or something.........

2

Yes

YOUR BRAIN EXPLODING

This is VERY nearly identical to a question you asked yesterday with the Statue of Liberty.....why don't YOU try to answer it and tell us what you find....then we can help YOU LEARN how to do your homework !!!    OK???

We need to deal in the same units.....24 inches = 2 ft....so....

2 ft : 1454 ft   =

1 ft :  727 ft  =

1 : 727