Triangle - high school - problems

  1. Children playground
    lich_5 The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.
  2. Cube cut
    cut_cube In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
  3. Vertices of a right triangle
    right_triangle_5 Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle
  4. Depth angle
    cliff From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?
  5. Infinite sum of areas
    height-of-equilateral-triangle Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tri
  6. Circle described
    described_circle_right_triangle The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
  7. Axial cut of a rectangle
    cylinder_cut Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
  8. Trapezoid MO
    right_trapezium The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
  9. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
  10. Circle chord
    circleChord What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
  11. Rectangle
    rectangle_inscribed_circle The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
  12. Trigonometric functions
    trigonom In right triangle is: ? Determine the value of s and c: ? ?
  13. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
  14. Triangle SAS
    triangle_iron Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°.
  15. Gimli Glider
    gimli_glider Aircraft Boeing 767 lose both engines at 44000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 2000 feet and maintain constant speed 196 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
  16. River
    river From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.
  17. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 7 cm.
  18. Right triangle Alef
    r_triangle The area of a right triangle is 294 cm2, the hypotenuse is 35 cm long. Determine the lengths of the legs.
  19. Square and circles
    kruznica_stvorec_1 Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
  20. Observer
    ohrada The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence?

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