# Tagged Questions

0answers
31 views

### How to find Latitudes and Longitudes of projections of the vertices of a rectangular plane below earth's surface?

I want to find out the latitudes and longitudes of projections of the vertices of a rectangular plane inside the earth's surface. I know dimensions of rectangle, angles of orientation and latitude and ...
2answers
77 views

### Computing distance from line to point in geodetic environment

Supposing to be in a cartesian plan and that I have the following point: $$A(x_{1},y_{1}), B(x_{2},y_{2}), C(x_{3},y_{3}), D(x_{4},y_{4})$$ $$P(x_{0},y_{0})$$ Now immagine two lines, the fist one ...
2answers
878 views

### Different ways for calculating distance between two geodetic points give me different results

I'm trying to calculate the distance between two geodetic points in two different ways. The points are: A:(41.466138, 15.547839) B:(41.467216, 15.547025) The ...
1answer
55 views

### Which icosahedral triangles projected onto sphere's surface contain points in P?

I am working on a Python script to: Compute the vertex coordinates of a geodesic sphere/icosahedron, Project the triangles onto a sphere, then Find which spherical triangle contains an arbitrary ...
2answers
722 views

### Determine depth of a partially filled hemisphere

Recently came across a question in a Year 9 math book of which there was no "working out" supplied and offers now description on how they obtained the answer. The question goes like this: A bowl ...
1answer
38 views

### approximation of law sines from spherical case to planar case

we know for plane triangle cosine rule is $\cos C=\frac{a^+b^2-c^2}{2ab}$ and on spherical triangle is $\cos C=\frac{\cos c - \cos a \cos b} {\sin a\sin b}$ suppose $a,b,c<\epsilon$ which are ...
1answer
70 views

### The law of cosines for a sphere

$\cos(c) = \cos(a)\cos(b) + \sin(a)\sin(b)\cos(C)$ Prove that if $a$, $b$, and $c$ is approximately $0$, then $c^2 = a^2 + b^2 - 2ab~\cos(C)$. I wasn't sure how to prove this. One thought I had was ...
1answer
208 views

### Distance measurement between latitude/longiture pairs.

I need to calculate the distance between two lat/lng coordinate pairs. In addition, If given an initial lat/lng coordinate, angle of travel, and distance, I need to calculate the resulting lat/lng ...
1answer
235 views

### Circle on sphere

Foreword This question was inspired by initial mistakes in this question. I wanted to explore the strange circle with $A>\pi r^2$ and got lost into geometrical jungle. A spherical cap is usually ...
1answer
2k views

### Angle between GPS coordinates

I realize GPS Coordinates are spherical coordinates. However I know the earth is more of an ellipsoid. I need to compute with a fairly high degree of accuracy the pitch and yaw between two objects ...
1answer
170 views

### Sine rule and equal angles

Is it true that if a triangle on a unit sphere has 2 sides with equal length then their opposit angles must be equal? I think it is true. I think we can use the spherical sine law. Call the sides with ...
1answer
330 views

### I have equations for getting x,y,z given latitude, longitude, and altitude. How do I reverse them?

I am using equations that look like the following to get x, y, and z given latitude, longitude, and altitude. ...
1answer
684 views

### Using the spherical law of cosines

Compute angular length c of the great-circle route between these two cities: Daytona Beach (location A): $29^\circ12'\ N, 81^\circ1' \ W$. Sidi Ifni (location B): \$29^\circ23' \ N. 10^\circ10' \ ...
2answers
3k views

### Napier's Rules applied to spherical distance calculations

I was in the middle of writing the same old geographic distance calculation using the Haversine formula when it occurred to me: shouldn't there be simpler way to do this? Haversine is of course ...
1answer
883 views

### How to calculate a heading on the earths surface?

Given an initial position and a subsequent position, each given by latitude and longitude in the WGS-84 system. How do you determine the heading in degrees clockwise from true north of movement?