Diagonal + right triangle - math problems

Number of problems found: 225

Two cables
On a flat plain, 2 columns are erected vertically upwards. One is 7 m high and the other 4 m. Cables are stretched between the top of one column and the foot of the other column. At what height will the cables cross? Assume that the cables do not sag.
Distance of lines
Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm
Deviation of the lines
Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm
Area of iso-trap
Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other.
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?
Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
Construct rhombus
Construct rhombus ABCD if given diagonal length | AC | = 8cm, inscribed circle radius r = 1.5cm
Company logo
The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo?
Rhombus ABCD
Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
Trapezoid MO
The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid.
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
Tetrahedral pyramid
It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor and
Angle of the body diagonals
Using vector dot product calculate the angle of the body diagonals of the cube.
MO Z8–I–6 2018
In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line.
Square pyramid
Calculate the pyramid's volume with the side 5cm long and with a square base, side-base has an angle of 60 degrees.
Regular hexagonal prism
Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
Faces diagonals
If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), then find the cuboid volume. Solve for x=1.3, y=1, z=1.2
The sides
The sides of the rectangle are in a ratio of 3: 5 and its circumference measures 72 cm. Calculate: a) the size of both sides of the rectangle b) the area of the rectangle c) the length of the diagonals
Side edges
The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid.