{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 3: Trilateration"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.1: 4.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"clc; funcprot(0);\n",
"// Initialization of Variable\n",
"AB=25145.32;//distance in m\n",
"R=6370.0e3;//radius of earth in m\n",
"ha=325.14;//elevation in m\n",
"//calculation\n",
"theta=AB*cos(3+9.0/60+40.0/3600)/R;\n",
"AB_dash=AB/sin(%pi/2+theta/2)*sin(%pi/2-theta/2-(3+9.0/60+40.0/3600)*%pi/180);\n",
"CD=AB_dash-AB_dash*ha/R;\n",
"S=CD+CD**3/24.0/R**2;\n",
"disp(S,'sea level length in m')\n",
"clear()\n",
"disp('answer varies slightly due to round off error')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.2: 5.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"clc; funcprot(0);\n",
"// Initialization of Variable\n",
"AB=31325.14//slope distance in m\n",
"R=6370.0e3;//radius of earth\n",
"ha=1582.15;//elevation in m\n",
"h=4251.32-ha//in m\n",
"//calculation\n",
"AB_dash=AB-h**2/2/AB;\n",
"theta=2*asin(AB_dash/2/R);\n",
"AB_dash=AB-(h*sin(theta/2)+h**2/AB/2)\n",
"CD=AB_dash-AB_dash*ha/R;\n",
"S=CD+CD**3/24.0/R**2;\n",
"disp(S,'sea level length in m')\n",
"clear()"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.3: 6.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"clc; funcprot(0);\n",
"// Initialization of Variable\n",
"//alpha=A and beta=B and those are angles\n",
"AB=1525.456;//distance in m\n",
"BC=2176.945;//distance in m\n",
"CD=1697.435;//distance in m\n",
"AD=2401.435;//distance in m\n",
"AC=3073.845;//distance in m\n",
"BD=2483.115;//distance in m\n",
"//calculation\n",
"A1=acos((CD**2+AC**2-AD**2)/(2*CD*AC));\n",
"A1=A1*180/%pi;\n",
"A2=acos((AD**2+BD**2-AB**2)/(2*AD*BD));\n",
"A2=A2*180/%pi;\n",
"A3=acos((AB**2+AC**2-BC**2)/(2*AB*AC));\n",
"A3=A3*180/%pi;\n",
"A4=acos((BC**2+BD**2-CD**2)/(2*BC*BD));\n",
"A4=A4*180/%pi;\n",
"B1=acos((CD**2+BD**2-BC**2)/(2*CD*BD));\n",
"B1=B1*180/%pi;\n",
"B2=acos((AD**2+AC**2-CD**2)/(2*AD*AC));\n",
"B2=B2*180/%pi;\n",
"B3=acos((AB**2+BD**2-AD**2)/(2*AB*BD));\n",
"B3=B3*180/%pi;\n",
"B4=acos((AC**2+BC**2-AB**2)/(2*AC*BC));\n",
"B4=B4*180/%pi;\n",
"e1=360-A1-A2-A3-A4-B1-B2-B3-B4;//error\n",
"e2=A1+B1-A3-B3;//error\n",
"e3=A2+B2-A4-B4;//error\n",
"//angle update\n",
"A1=A1+e1/8-e2/4;\n",
"A3=A3+e1/8+e2/4;\n",
"B1=B1+e1/8-e2/4;\n",
"B3=B3+e1/8+e2/4;\n",
"A2=A2+e1/8-e3/4;\n",
"B2=B2+e1/8-e3/4;\n",
"A4=A4+e1/8+e3/4;\n",
"B4=B4+e1/8+e3/4;\n",
"//updating sides\n",
"AD=1525.456*sin(B3*%pi/180)/sin(A2*%pi/180);\n",
"disp('equation for B2 is wrong')\n",
"disp(AD,'corrected length of AD in m')\n",
"BD=1525.456*sin(A3*%pi/180+B2*%pi/180)/sin(A2*%pi/180);\n",
"disp(BD,'corrected length of BD in m')\n",
"AC=1525.456*sin(A4*%pi/180+B3*%pi/180)/sin(B4*%pi/180);\n",
"disp(AC,'corrected length of AC in m')\n",
"BC=1525.456*sin(A3*%pi/180)/sin(B4*%pi/180);\n",
"disp(BC,'corrected length of BC in m')\n",
"CD=BC*sin(A4*%pi/180)/sin(B1*%pi/180)\n",
"disp(CD,'corrected length of CD in m')\n",
"disp('answers differ slightly due to value of pi');\n",
"//equation for B2 is wrong\n",
"clear()"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.4: 7.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"clc; funcprot(0);\n",
"// Initialization of Variable\n",
"//angles found by cosine law\n",
"//alpha=A and beta=B and those are angles\n",
"A1=45.801596;//distance in m\n",
"A2=40.605250;//distance in m\n",
"A3=50.143258;//distance in m\n",
"A4=43.077646;//distance in m\n",
"B1=48.779868;//distance in m\n",
"B2=44.141587;//distance in m\n",
"B3=49.733152;//distance in m\n",
"B4=37.737035;//distance in m\n",
"//calculation\n",
"e1=360-A1-A2-A3-A4-B1-B2-B3-B4;//error\n",
"//angle update\n",
"A1=A1+e1/8;\n",
"A3=A3+e1/8;\n",
"B1=B1+e1/8;\n",
"B3=B3+e1/8;\n",
"A2=A2+e1/8;\n",
"B2=B2+e1/8;\n",
"A4=A4+e1/8;\n",
"B4=B4+e1/8;\n",
"E2=(log(sin(A1*%pi/180))*log(sin(A2*%pi/180))*log(sin(A3*%pi/180))*log(sin(A4*%pi/180))-log(sin(B1*%pi/180))*log(sin(B2*%pi/180))*log(sin(B3*%pi/180))*log(sin(B4*%pi/180)))/log(10000);\n",
"c3=E2/17.1;\n",
"c4=E2/17.0;\n",
"A1=A1-c3;\n",
"disp(A1,'corrected angle A1 in degrees')\n",
"B1=B1+c3;\n",
"disp(B1,'corrected angle B1 in degrees')\n",
"clear()"
   ]
   }
],
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		   "file_extension": ".sce",
		   "help_links": [
			{
			 "text": "MetaKernel Magics",
			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
			}
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