1. ΔABC is an equilateral triangle. Side AB makes 45° with a plane α and side AC lies in plane α. What is the tangent of the angle between planes (ABC) and α ? 2. Given a rhombus with diagonals 10 cm and 4 cm. The angle between the plane of rhombus and the projection plane is 60°. Find the area of the projection of the rhombus.
3.In the plane α, consider the points B, C and E so that BC = 9 cm, CE = 12 cm and BE = 15 cm. Let A be a point not in plane α such that AB ⊥ α and AB = 36 cm.
a. Find the angle between line CE and plane ABC.
b. Find the tangent of the angle between planes ACE and BCE.
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