Problems of the triangle

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. The sum of the measures of the interior angles of a triangle is always 180 degrees. An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The best known area formula is T = a*h /2 where a is the length of the side of the triangle, and h is the height or altitude of the triangle.

Number of problems found: 1300

  • Pyramid cut
    We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the
  • Earth's circumference
    Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
  • Circular pool
    The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool?
  • Hexagon cut pyramid
    Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge is 12 cm, and the side edge length is 41 cm.
  • Secret treasure
    Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure.
  • Conical bottle
    When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
  • Cutting cone
    A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm.
  • Right circular cone
    The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base.
  • The truncated
    The truncated rotating cone has bases with radii r1 = 8 cm, r2 = 4 cm and height v = 5 cm. What is the volume of the cone from which the truncated cone originated?
  • 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.
  • Angle of two lines
    There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV.
  • Airplane
    Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
  • Forces
    In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N, and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2, and F3.
  • Distance of lines
    Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm
  • Solid cuboid
    A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
  • CoG center
    Find the position of the center of gravity of a system of four mass points having masses, m1, m2 = 2 m1, m3 = 3 m1, and m4 = 4 m1, if they lie at the vertices of an isosceles tetrahedron. (in all cases, between adjacent material points, the distance
  • Angle of the body diagonals
    Using vector dot product calculate the angle of the body diagonals of the cube.
  • Vector
    Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
  • Ladder
    4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
  • Sphere equation
    Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).

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See also our trigonometric triangle calculator. See also more information on Wikipedia.