# Trigonometry word problems?

• Nov 11th 2012, 01:27 PM
SoConfused123
Trigonometry word problems?
1.Circumference of earth is 25,000 mi. At an altitude of 35,000 ft. directly from the NP to a point on the equator, what is the distance traveled?
• Nov 11th 2012, 01:46 PM
skeeter
Re: Trigonometry word problems?
(1) arclength ... $s = r\cdot \theta$ , where $\theta$ is in radians

how many radians in a quarter circle?

(2) I believe the formula , $A_x = x\tan \left(\frac{180}{x} \right)$ is for a circle inscribed in a polygon of x sides.

A(6) = 3.464...

A(10) = 3.249...

A(100) = 3.1426...

A(1000) = 3.1416...

A(10000) = 3.14159...

so ... what value is this approaching?

(3) yes, 30 ft = distance from crest to trough ...double the amplitude.
• Nov 11th 2012, 02:21 PM
SoConfused123
Re: Trigonometry word problems?
1. There's pi/2 radians in quarter of a circle?

2.So it would be approaching pi?
• Nov 11th 2012, 02:29 PM
skeeter
Re: Trigonometry word problems?
Quote:

Originally Posted by SoConfused123
1. There's pi/2 radians in quarter of a circle?

why the question mark? you should know this ...

2.So it would be approaching pi?

sure looks that way ... do you understand what's happening here in a geometrical sense?

...
• Nov 11th 2012, 02:39 PM
SoConfused123
Re: Trigonometry word problems?
1. I know, I should.
So S= r * pi/2

So since I have the circumference of the earth being approx. 25,000 mi. would I do 25,000/pi/2= 3978.87 as the radius
and do 3978.87*pi/2 = 6,250 miles as distance traveled?
Or am I way off?

2.I think so.
• Nov 11th 2012, 02:55 PM
skeeter
Re: Trigonometry word problems?
(1) radius of the earth, $R_e = \frac{25000}{2\pi}$

the pilot's radius is $R_p = R_e + 35000 \, ft = \frac{25000}{2\pi} + \frac{35000}{5280}$

$d = R_p \cdot \frac{\pi}{2}$

(2) as the polygon gets more and more sides, it starts to look like a circle ... what's the area of a unit circle?
• Nov 11th 2012, 03:14 PM
SoConfused123
Re: Trigonometry word problems?
1. So around 61,695 miles would be the distance traveled. Is that right?

2. A= pi * r2
So pi*12= pi
A= pi
• Nov 11th 2012, 03:20 PM
skeeter
Re: Trigonometry word problems?
Quote:

Originally Posted by SoConfused123
1. So around 61,695 miles would be the distance traveled. Is that right?

check it again ... how can traveling about 1/4 of the earth's circumference be greater than the earth's circumference?
• Nov 11th 2012, 03:37 PM
SoConfused123
Re: Trigonometry word problems?
Ah, true.
I typed it in as radians the first time.

This time I typed it in as degrees
69.44+6.62=76.06 * 90º = 6,845 miles

Is that correct now?
• Nov 11th 2012, 03:41 PM
skeeter
Re: Trigonometry word problems?
$\left(\frac{25000}{2\pi} + \frac{35000}{5280}\right) \cdot \frac{\pi}{2} = 6260 \, miles$
• Nov 11th 2012, 03:47 PM
SoConfused123
Re: Trigonometry word problems?
Blaghfgdgf.
I typed it in just like you showed it and it still won't come out to your answer.
Well thank you so much for your help, I'll keep working on it.
• Nov 11th 2012, 03:52 PM
skeeter
Re: Trigonometry word problems?
Quote:

Originally Posted by SoConfused123
Blaghfgdgf.
I typed it in just like you showed it and it still won't come out to your answer.
Well thank you so much for your help, I'll keep working on it.

put the $(2\pi)$ in parenthesis ...
• Nov 11th 2012, 03:56 PM
SoConfused123
Re: Trigonometry word problems?
Ahh, got it.
Thanks. :)