Trigonometry

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October 10th 2006, 03:35 PM
Nikkipoo

Trigonometry

Question 1:

In this question, use pie=3.14 and assume the earth to be a sphere of radius 6370km. The towns A and B are both on the circle of latitude 24° N. the longitude of A is 108° E and the longitude of B is 75° E.

Calculate , correct to the nearest kilometre,
a) the radius of the circle of latitude 24° N

b) the shortest distances between A and B, measured along the circle of latitude 24 ° N.

Question 2:

In this question assume that the earth is a sphere of radius 6370km.
The four arcs on the digram represent the equator, the Greenwich Meridian, latitude 6° N and latitude 52° N.

a) the Greenwich Meridian passes through London (52°N,0) and Accra(6°N,0).

i) Calculate to the NEAREST kilometre, the shortest distance between London and Accra along thier common circle of longitude. use pie= 3.14.
c) Tropical Strom Kyle was reported to be located 5 470km due west of Accra.
i) Calculate to radius of the circle of latitude on which K lies.
October 10th 2006, 05:46 PM
Quick

Quote:

Originally Posted by Nikkipoo

Question 1:

In this question, use pie=3.14 and assume the earth to be a sphere of radius 6370km. The towns A and B are both on the circle of latitude 24° N. the longitude of A is 108° E and the longitude of B is 75° E.

Calculate , correct to the nearest kilometre,
a) the radius of the circle of latitude 24° N

I believe that lattitude is measured by the arc from the lattitude line to the equator.

With this in mind, draw a circle P.

Draw the diameter of the circle.

Now Label the points that are formed A and E

Now draw a ray from point P that crosses the circle at point B such that APB=24 degrees.

Now draw a ray from point P that crosses the circle at point D such that DPE=24 degrees (this line needs to be on the same side of the diameter as ray PB)

Now draw a line connecting points B and D

That line represents a side view of Lattitude 24

Now draw a line that's perpindicular to AE and intersects BD at point C

Notice that that line is also perpindicular to BD

Thus PCD is 90 degrees

And CPD is 66 degrees.

And you know that PD is 6370km

Thus CD is sin(66) times 6370km

Note that CD is the radius of the circle formed at 24 degrees north.

Thus the radius is 6370sin(66) which equals approximately 5819km
October 11th 2006, 01:49 AM
earboth

2 Attachment(s)

Question 1 only

Quote:

Originally Posted by Nikkipoo

Question 1:

In this question, use pie=3.14 and assume the earth to be a sphere of radius 6370km. The towns A and B are both on the circle of latitude 24° N. the longitude of A is 108° E and the longitude of B is 75° E.

Calculate , correct to the nearest kilometre,
a) the radius of the circle of latitude 24° N

b) the shortest distances between A and B, measured along the circle of latitude 24 ° N.
...

Hi,

a) I've attache a diagram to show you how I calculated the radius of the circle at 24° latitude:

r = R * cos(24°). Plug in the value you know and you'll get:

r = 6370 km * cos(24°) = 5819 km as Quick has already calculated.

b) the points A and B lay on the circumference of the circle at latitude 24°. The difference between these points is 33°. The circumference of this circle is:

c = 2 * pi * 5819 km = 36543 km

Let d be the distance between A and b. Now you have the proportion:

c / 360° = d / 33° . Solve for d:

d = (c * 33°) / (360°) = 3350 km
October 11th 2006, 01:56 AM
earboth

Question 2 only

Quote:

Originally Posted by Nikkipoo

...
Question 2:
In this question assume that the earth is a sphere of radius 6370km.
The four arcs on the digram represent the equator, the Greenwich Meridian, latitude 6° N and latitude 52° N.
a) the Greenwich Meridian passes through London (52°N,0) and Accra(6°N,0).
i) Calculate to the NEAREST kilometre, the shortest distance between London and Accra along thier common circle of longitude. use pie= 3.14.
c) Tropical Strom Kyle was reported to be located 5 470km due west of Accra.
i) Calculate to radius of the circle of latitude on which K lies.

Hi,

use the method I've shown to you in my previous reply:

Distance between London (L) and Accra (A) is d. The difference between L and A is 46°.

You have the proportion:

d / 46° = (2 * pi * 6370 km) / 360°. Solve for d. (5112 km)

The radius of the circle at latitude 6°N is calculated:

r = 6370 km * cos(6°) = 6335 km