Triangle + expression of a variable from the formula - math problems

  1. TV tower
    Žižkov_tv_tower Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°?
  2. The ladder
    rebrik The ladder touch on a wall at a height of 7.5 m. The angle of the inclination of the ladder is 76°. How far is the lower end of the ladder from the wall?
  3. Cutting cone
    kuzel_zrezany 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.
  4. Telegraph poles
    pole The bases of two adjacent telegraph poles have a height difference of 10.5 m. How long do the wires connect the two poles if the slope is 39° 30´?
  5. Height of pyramid
    ihlan The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height?
  6. Circle and square
    square_axes An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
  7. Viewing angle
    zorny The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
  8. Side lengths
    triangles_1 In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.
  9. Observation tower
    ship_1 From the observation tower at a height of 105 m above sea level, the ship is aimed at a depth angle of 1° 49´. How far is the ship from the base of the tower?
  10. Triangle from median
    triangles_1 Calculate the perimeter, content, and magnitudes of the remaining angles of triangle ABC, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
  11. Interior angles
    triangles_1 Calculate the interior angles of a triangle that are in the ratio 2: 3: 4.
  12. The right triangle
    rt_tr540 The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. Calculate the length of the leg b and the median t2 to side b.
  13. Concentric circles and chord
    tetiva2 In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?
  14. In a
    triangles_1 In a triangle, the aspect ratio a: c is 3: 2 and a: b 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides.
  15. The bases
    rr_lichobeznik The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid.
  16. The angles ratio
    123_triangle The angles in the ABC triangle are in the ratio 1: 2: 3. find the sizes of the angles and determine what kind of a triangle it is.
  17. Spherical cap
    Spherical_cap The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut.
  18. A kite
    sarkan Children have a kite on an 80m long rope, which floats above a place 25m from the place where children stand. How high is the dragon floating above the terrain?
  19. Height to the base
    triangle The triangle area is 35 cm ^ 2. The size of the base is 10 cm. Find the length of height to the base.
  20. An equilateral
    rs_triangle2 An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?

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