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AB and CD are the two straight roads , across each other at P at ${{75}^{\circ }}$angle. 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 at equal distance from P and X, and is also at equal distance from the roads.
AB and CD are the two straight roads , across each other at P at ${{75}^{\circ }}$angle. 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 at equal distance from P and X, and is also at equal distance from the roads.
Class 10 | Frank | Guides | ICSE | Loci | Maths
AB and CD are the two straight roads , across each other at P at ${{75}^{\circ }}$angle. 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 at equal distance from P and X, and is also at equal distance from the roads.

Steps of construction:

ATQ,

1. Let us Draw two lines AB and CD crossing at an angle of ${{75}^{\circ }}$

2. Then draw an angle bisector of $\angle BPD$ with the help of compass

3. Now, draw perpendicular from X on angle bisector with the help of compass ,meeting at O.

4. From point Y, $PX=PY$, draw a perpendicular on angle bisector with the help of compass, meeting at O.

5. So, O is the point which Equal distance from P, X and both the roads.

We know,  $\cos \theta =$hypotenuse/base

$cos(37.5)=PO/800$

$0.980243=PO/800$

$PO=0.980243×800$

$PO=784.19m$

Hence $PO=784.19 m$

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