Sine + triangle - math problems

  1. What percentage
    astronaut 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
  2. Power line pole
    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.
  3. Steps
    steps_1 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.
  4. Tetrahedral pyramid
    ihlan Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.
  5. The aspect ratio
    triangles The aspect ratio of the rectangular triangle is 13: 12: 5. Calculate the internal angles of the triangle.
  6. Isosceles triangle 10
    iso_23 In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.
  7. The hemisphere
    naklon_koule The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
  8. The ladder
    rebrik The ladder has a length of 3 m and is leaning against the wall, and its inclination to the wall is 45°. How high does it reach?
  9. The cable car
    lanovka The cable car has a length of 3,5 kilometers and an angle of climb of 30 degrees. What is the altitude difference between Upper and Lower Station?
  10. One side
    angle_incline One side is 36 long with a 15° incline. What is the height at the end of that side?
  11. Right triangle
    rebrik_7 Ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard?
  12. Mast shadow
    horizons Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
  13. An angle
    right_triangle_6 An angle x is opposite side AB which is 10, and side AC is 15 which is hypotenuse side in triangle ABC. Calculate angle x.
  14. 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.
  15. Diagonals of the rhombus
    kosostvorec_3 How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm2?
  16. Diagonals of pentagon
    5gon_diagonal Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
  17. Deviation of the lines
    kvadr_1 Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm
  18. Decagon
    decanon Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
  19. SSA and geometry
    ssu_veta The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer.
  20. Right triangle
    rt_A Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.

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Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation. See also our trigonometric triangle calculator.