Cosine + triangle - math problems

  1. Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  2. 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
  3. 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.
  4. 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.
  5. The spacecraft
    Sputnik_670 The spacecraft spotted a radar device at altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered
  6. 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´.
  7. The aspect ratio
    triangles The aspect ratio of the rectangular triangle is 13: 12: 5. Calculate the internal angles of the triangle.
  8. A rhombus
    rhombus-diagonals2 A rhombus has sides of length 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus.
  9. 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.
  10. 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?
  11. One side
    angle_incline One side is 36 long with a 15° incline. What is the height at the end of that side?
  12. Isosceles triangle 8
    7-6-7-triangle If the rate of the sides an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree.
  13. 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.
  14. Calculate 2
    t_sss Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm
  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. The pond
    rybnik_3 We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
  18. 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'.
  19. Road
    12perctent The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
  20. Regular quadrangular pyramid
    ihlan The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes?

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