Question 1203521: Town Q is 11km due east of town P,while town R is 7km on the bearing of S65°E of town P.(a) using scale drawing, show the position of P,Q and R use a scale of 1cm to 1km
(b) from your drawing, measure and record the distance between Q and R.
Found 3 solutions by Theo, ikleyn, math_tutor2020:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's my schematic followed by my calculations followed by my scale drawing.
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.
Answer by ikleyn(52835)  (Show Source):
You can put this solution on YOUR website! .
Looking at this problem, I do not understand for which reason @Theo made his calculations, at all.
The problem does not assume making any calculations.
It assumes making a plot, only, which is NOT a Math problem, at all.
Simply the visitor wants that the tutors make his job - plotting this figure for him, for free.
He does not want anything else.
Simply a capital slacker, and @Theo helps him, working instead of him - nothing else.
Such posts should be destroyed as irrelevant to the goals of this forum,
and their senders subjected to a legal fine.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
PQ = 11
PR = 7
QR = x
Law of cosines
c^2 = a^2 + b^2 - 2ab*cos(C)
x^2 = 7^2 + 11^2 - 2*7*11*cos(25)
x^2 = 30.428600796356
x = sqrt(30.428600796356)
x = 5.5162125408976
The distance from Q to R is about 5.516 km.
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