Cosine + Pythagorean theorem - 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. 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´.
  4. The aspect ratio
    triangles The aspect ratio of the rectangular triangle is 13: 12: 5. Calculate the internal angles of the triangle.
  5. Coordinates of square vertices
    rotate_square I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter.
  6. 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?
  7. 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?
  8. 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?
  9. Right angled triangle 3
    right_triangle_3 Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
  10. Two forces
    forces_1 The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
  11. The mast
    octagon A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
  12. Square pyramid
    pyramid_4 Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
  13. Angle of deviation
    kuzel2_1 The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
  14. Right triangle trigonometrics
    triangle2 Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
  15. 30-gon
    30gon At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
  16. Regular n-gon
    regular_polygons Which regular polygon have a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm?
  17. Resultant force
    3forces Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
  18. Forces
    vectors_4 Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
  19. Bearing
    compass A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
  20. Right triangle
    rt_triangle It is given a right triangle angle alpha of 90 degrees beta angle of 55 degrees c = 10 cm use Pythagorean theorem to calculate sides a and b

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Pythagorean theorem is the base for the right triangle calculator.