Check Yourself 13

1. Given an equilateral triangle ABC where G is the centroid. Point N is not in the plane of ΔABC and NG is perpendicular to the plane of ΔABC. The angle between NA and NG is 30°. If NG = cm, find side length of ΔABC.

2. Given point M and plane α such that M ∉ α. MO is perpendicular to plane α. MP and MQ are inclined to α which make 45° and 60° with plane α, respectively. Find the length of PQ in terms of MO if ∠POQ = 150°.

3. ΔABC is a right triangle with ∠C = 90°, ∠A = 30°, and AC = 3 cm. Line segment DC is perpendicular to the plane of ΔABC. If DC = cm, find the angle between (ADB) and (ABC).

4. On the faces of a dihedral angle taken 2 points which are at a distance of 6 cm and 10 cm from the edge of the dihedral angle. The distance from one of the points to the opposite face is 7,5 cm. Find the distance between the second point and its opposite face.

5. 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?

6. In the adjacent figure, an equilateral triangle ABC is given. Point P is not lying in the plane of ΔABC and

PA = PB = PC = AB.

Find the cosine of the dihedral angle formed by any two faces.

Дата добавления: 2015-07-20