Cosine + diagonal - practice problems
Number of problems found: 30
- Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls.
- One of
One of the internal angles of the rhombus is 120° and the shorter diagonal is 3.4 meters long. Find the perimeter of the rhombus.
- Parallelogram diagonals
Find the area of a parallelogram if the diagonals u1 = 15 cm, u2 = 12 cm and the angle formed by them is 30 degrees.
- A rectangle 5
A rectangle has sides of 10 cm and 14 cm. Calculate the angle between a diagonal and alongside.
- Angle of diagonals
Calculate the perimeter and the area of a rectangle if its diagonal is 14 cm and the diagonals form an angle of 130°.
- Base diagonal
In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid.
- Space diagonal angles
Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD.
- Rhombus diagonals
In the rhombus ABCD are given the sizes of diagonals e = 24 cm; f = 10 cm. Calculate the side length of the diamond and the size of the angles, calculate the content of the diamond
- Distance of points
A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S.
- Quadrilateral oblique prism
What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°.
- Triangle in a square
In a square ABCD with side a = 6 cm, point E is the center of side AB, and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides.
- Angle of the body diagonals
Using vector dot product calculate the angle of the body diagonals of the cube.
- A rhombus
A rhombus has sides of length 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus.
- Diagonals of the rhombus
How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm²?
- Diagonals of pentagon
Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
- Square pyramid
Calculate the pyramid's volume with the side 5 cm long and with a square base, and the side-base has an angle of 60 degrees.
Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
- Trapezoid IV
In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD?
- Diagonals in diamond
In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
- Diamond ABCD
In the diamond ABCD, the diagonal e = 24 cm and the size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond.
Cosine - practice problems. Diagonal - practice problems.