# 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.

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