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Question
Two straight roads AB and CD cross each other at Pat an angle of 75° . X is a stone on the road AB, 800m from P towards B. BY taking an appropriate scale draw a figure to locate the position of a pole, which is equidistant from P and X, and is also equidistant from the roads.
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Solution
Steps of construction:
(i) Draw two lines AB and CD crossing at an angle of 75 °
(ii) Draw an angle bisector for ∠ BPD
(iii) Draw perpendicular from X on angle bisector meeting at 0.
(iv) From point Y, PX = PY, draw a perpendicular on angle bisector meeting at 0.
(v) 0 is the point which is equidistant from P, X and both the roads.
cos θ = `"hypotenuse"/"base"`
cos `75/2 = "PO"/"PX"`
cos (37.5) = `"PO"/800`
0.980243 = `"PO"/800`
PO = 784.19 m
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