2015 · Q65
An equilateral triangle BOC is drawn inside a square ABCD. If angle AOD=2θ, what is tanθ equal to ?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A2-{3}
- B1+{2}
- C4-{3}
- D2+{3}
Explanation
With side 1, O = (1 - sqrt(3)/2, 1/2); cos(angleAOD) = -sqrt(3)/2 gives angleAOD = 150 deg = 2*theta, so theta = 75 deg and tan75 = 2 + sqrt(3). Hence option (d).