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In the diagram angle AOB=60 degrees and point P lies inside the angle. 



Line segments  PA and PB are drawn so they are perpendicular to the two rays forming angle O as shown. Given OA=a and OB=b find the distance OP in terms of a and b.

 

 May 16, 2020

Best Answer 

 #1
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Let d = OP.  Then cos POA = a/d and cos POB = b/d, so POA = acos(a/d) and POB = acos(b/d).

 

You can then write cos(acos(a/d) + acos(b/d)) = cos(60) = 1/2.

 

Since cos(x + y) = cos(x) cos(y) - sin(x) sin(y), you can then plug into this formula to solve for d.

 May 16, 2020
 #1
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Best Answer

Let d = OP.  Then cos POA = a/d and cos POB = b/d, so POA = acos(a/d) and POB = acos(b/d).

 

You can then write cos(acos(a/d) + acos(b/d)) = cos(60) = 1/2.

 

Since cos(x + y) = cos(x) cos(y) - sin(x) sin(y), you can then plug into this formula to solve for d.

Guest May 16, 2020

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