document.write( "Question 392634: a surveyor wishes to find the distance between two inaccessible points A&B on opposite side of the lake while standing at point C she finds that AC=259m ,BC=423inches and angle ABC measures 132 40' find the distance AB? \n" ); document.write( "
Algebra.Com's Answer #279399 by jsmallt9(3758)![]() ![]() ![]() You can put this solution on YOUR website! The Law of Cosines has four variables: the lengths of the 3 sides of a triangle and the measure of one angle. \n" ); document.write( "Your problem gives you 2 sides and the measure of one angle. So you know the values 3 of the 4 variables in the Law of Cosines. Anytime you know all but 1 variable in an equation you should be able to solve for the value of that last unknown. So we will use the Law of Cosines to solve this problem: \n" ); document.write( " \n" ); document.write( "To convert BC into meters, we divide by 39.37: \n" ); document.write( "BC = 423 inches = 432/39.37 meters = 10.7442214884429769 meters. \n" ); document.write( "Also 132 degrees and 40 minutes = 132.67 degrees since 40 minutes is 2/3 of a degree and 2/3 as a decimal is approximately 0.67. \n" ); document.write( "Inserting these values into our Law of Cosines equation we get: \n" ); document.write( " \n" ); document.write( "To avoid confusion I am going to replace (AB) with an \"x\": \n" ); document.write( " \n" ); document.write( "Simplifying we get: \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "This is a quadratic equation because of the \n" ); document.write( " \n" ); document.write( "Now we can use the Quadratic Formula: \n" ); document.write( " \n" ); document.write( "which simplifies as follows: \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "In long form this is: \n" ); document.write( " \n" ); document.write( "We can see that the second equation will give us a negative value. But the side of a triangle cannot be negative. So we will reject the second solution. The only solution we can use is: \n" ); document.write( " \n" ); document.write( "Using a calculator to find the square root we get: \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "x = 251.4661081380912442 \n" ); document.write( "So AB is approximately 251.5 meters long. \n" ); document.write( " |