Question 1203521
here's my schematic followed by my calculations followed by my scale drawing.


<img src = "http://theo.x10hosting.com/2023/090701.jpg">


in the schedmatic, i drew points A, B, and C, in addition to points P, Q, R.


points P, B, R, A, formed a rectangle.
points B, Q, C, R, formed another rectangle.


south 65 east forms angle RPA. in triangle APR.since.
angle PRA + angle RPA = 90 degrees.
therefore angle PRA is equal to 25 degrees.


x is the vertical leg of triangle APR and y is the hozizontal leg of triangle APR.
since trangle APR is a right triangle, you can use trigonometry to find the length of x and y.
x = 7 * sin(25) and y = 7 * cos(25).


thos values are stored in the calculator for future use.
displayed is a truncated version of the values stored.
you can use your calculator to derive the full values of x and y, if you need to have it.
i used the stored values in all calculations that reuire the values of x and y and 11-y and z.


since PQis 11 km, and y is 6.3442 km, then 11 - y = 4.6558 km.


triangle RQC is a nother right triangle with the vertical leg equal to x and the horizontal leg equal to 11 - y.
i used the pythatorus theorem to find the value of z.
z is the distance between R and Q.
that distance is equal to 5.5162 km.


further down in the diagram, i used the scale of 1 km in real life to 1 cm on paper.
i drew PQ as 11 cm.
i drew PA as 2.96 cm.
i drew AR as 6.34 cm.
i drew PR as 7 cm and also verified that the measurement was correct based on the scale ratio.
i then drew RQ and measured tha distance.
it was 5.51 cm, as it should be qith a scale of 1 km to 1 cm.


everything seems to check out, so i'll go with what i provided.
it should be good.
you may check it out to see if you agree.