PQ is a diameter of a circle whose centre is O.R is a point on the circumference such that the chord PR=12cm and the chord RQ=5cm.Find angle RPQ in rad.Calculate angle RPQ in Radians.  

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should notice that the central angle POQ is of 180 degrees, since PQ is diameter of circle. The angle PRQ is half the central angle POQ, hence PRQ = `90^o` .

Since triangle POQ is right, then diameter PQ denotes the hypotenuse and the chords PQ , RQ denote the legs of triangle.

You need to use the tangent or cotangent functions to find RPQ, because you know the lengths of the legs and it is of no use to find the length of hypotenuse and then to use sine or cosine functions (there would be more steps to follow and the process of solving would take longer time).

Using cotangent function yields: cot RPQ = PR/RQ => cot RPQ = `12/5 ` => cot RPQ = 2.4 => RPQ `~~ 0.39`  radians.

Hence, the angle RPQ is about of 0.39 radians.

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nathanshields's profile pic

nathanshields | High School Teacher | (Level 1) Associate Educator

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First recall that the angle PRQ must be right (pi radians) because it subtends a diameter.  So we have a right triangle with legs 12 and 5.  Using your trig ratios, you have angle RPQ = arctan(5/12) or about 0.395 radians.

ponka's profile pic

ponka | Student, Undergraduate | (Level 1) eNoter

Posted on

set ur calculator on radian mode then

tan-1 (12/5) = 0.395 ans

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