Question 279149
I don't know if there's an easier way to do this, but this is the way I did it.


Let the intersection of the two streets be point A.


Let the other end of the top street be point B so that the street is represented by the line segment AB.


Let the other end of the bottom street be point C so that the street is represented by the line segment AC.


You have a triangle called ABC where:


angle A is 52 degrees.
Line Segment AB is 60 meters.
Line Segment AC is 65 meters.


We drop a perpendicular from point B to intersect with line AC at point D.


We now have 2 triangles.


They are ABD and BDC.


Since we know angle A and we know AB = 60 meters, we can find the length of the line segment BD using the formula:


Sin(52) = BD / AB which becomes:


Sin(52) = BD / 60 because BD = 60 meters.


We solve for BD to get:


BD = 60 * Sin(52) which becomes:


BD = 47.28064522


We can also solve for AD using the formula:


Cos(52) = AD / AB which becomes:


Cos(52) = AD / 60  because AB = 60 meters.


We solve for AD to get:


AD = 60 * Cos(52) which becomes:


AD = 36.93968852


We now have AB and AD and BD and AC.


AB and AC were given.
AD and BD were solved for.


We know that AC = 65 meters and we know that AC = AD + DC and we know that AD = 36.93968852 so we can solve for BC using the formula:


DC = AC - AD which becomes:


DC = 65 - 36.93968852 which becomes:


DC = 28.06031148


Since we know BD and we know DC, we can now solve for angle C.


We use the formula:


Tan(C) = BD / DC which becomes:


Tan(C) = 47.28064522 / 28.06031148 which becomes:


Tan(C) = 1.684965088


We take the arctan(1.684965088) to find the angle.


Angle C = 59.31154245 degrees.


Now that we know angle C, we can use either BD or DC to find BC.


Either one will get the same answer.


Sin(C) = BD / BC


We solve for BC to get:


BC = BD / Sin(C) which becomes:


BC = 47.28064522 / Sin(59.341154245) which becomes:


BC = 54.98036461 meters.


We could also have used:


Cos(C) = DC / BC.


We solve for BC to get:


BC = DC / Cos(C) which becomes:


BC = 28.06031148 / Cos(59.31154245) which becomes:


BC = 54.98036461 which is the same answer we got before as it should be.


Your answer is:


The perimeter of the lot is:


AB + AC + BC which becomes:


60 + 65 + 54.98036461 = 179.9803646 meters.


A picture of what I just did is shown below:


<img src = "http://theo.x10hosting.com/problems/279149.jpg" alt = "********** PICTURE DID NOT DISPLAY PROPERLY **********" />


The + after the number indicates a fractional part that is not shown.


the part that's missing is AD = 36+.