Metric properties

2010015809

Level: 
B
The picture shows a square pyramid ABCDV. The side of a base square is a=6cm and the height of the pyramid is v=8cm. Find the angle φ between the opposite lateral edges (the angle AVC).
tg⁡φ2=328⟹φ≐⁡55∘53′
tg⁡φ=328⟹φ≐⁡27∘56′
tg⁡φ2=38⟹φ≐⁡41∘7′
tg⁡φ2=832⟹φ≐⁡124∘7′

2010015810

Level: 
B
The picture shows a square pyramid. The side of a base square is a=10cm and the height of the pyramid is v=10cm. Find the angle φ between the lateral edge and the edge of the base of the pyramid.
tg⁡φ=5⟹φ≐⁡65∘54′
tg⁡φ=55⟹φ≐⁡24∘6′
tg⁡φ2=55⟹φ≐⁡48∘11′
tg⁡φ=102⟹φ≐⁡57∘41′

9000046408

Level: 
B
Consider a cone of base radius r and a special shape: the shape is such that the volume of the cone is related to the base radius by the formula V=πr3. Find the angle between the side of the cone and the base. Round your answer to two decimal places.
71.57∘
45∘
63.43∘