Paper 2 · June 2018 · Circular measure

ABCD is a square of side $x$ cm, drawn with B and C as the upper vertices and A and D as the lower vertices, and O is the midpoint of AD. Find angle AOB in radians, correct to 3 decimal places.

Model answer

1,107

Also accepted: 1.107, 1,107 radians, 1.107 rad

Explanation

Triangle OAB is right angled at A with

OA=\frac{x}{2}

and

AB=x

, so

\tan(\angle AOB)=\dfrac{x}{x/2}=2

and

\angle AOB=\arctan 2=1{,}107

radians.

Derived from ZIMSEC Mathematics Paper 2, June 2018, Q1

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