Number of problems found: 526
- The angle of view
Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other.
- Two groves
Two groves A, B are separated by a forest, both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B, if AC = 5004 m, BC = 2600 m and angle ABC = 53° 45 ’?
- Decide 2
Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line
- Right angle
If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6
- Angle of the body diagonals
Using vector dot product calculate the angle of the body diagonals of the cube.
Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.
- What percentage
What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km
Lunch is given to seniors from 12:15 to 12:40 during the Coronavirus pandemic. What angle will the minute hand of clock describe during this time?
- Power line pole
From point A, the power line pole is seen at an angle of 18 degrees. From point B to which we get when going from point A 30m away from the column at an angle of 10 degrees. Find the height of the power pole.
Find the height between the two floors if you know that the number of steps between the two floors is 18, the gradient is 30º and the length of the step is 28.6 cm. Report the result in centimeters to the nearest centimeter.
- Magnitude of angle
What magnitude has an obtuse angle enclosed by the hands of clocks at 12:20 hours?
- Angle of cone
The cone has a base diameter of 1.5 m. The angle at the main apex of the axial section is 86°. Calculate the volume of the cone.
- Top of the tower
The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
- Triangular pyramid
A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
- Wall height
Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm.
- Hexa pyramid
The base of the regular pyramid is a hexagon, which can be described by a circle with a radius of 1 m. Find the volume of the pyramid 2.5 m high.
- Angled cyclist turn
The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn?
- Two bodies
The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Determine the ratio of surfaces of the first and seco
- A drone
A flying drone aimed the area for an architect. He took off perpendicularly from point C to point D. He was at a height of 300 m above the plane of ABC. The drone from point D pointed at a BDC angle of 43°. Calculate the distance between points C and B in
- Cone side
Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.