Right triangle - examples - page 8

  1. Pentagonal pyramid
    pyramid-pentagon Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
  2. Two balls
    balls-inside-cylinder Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
  3. Cone and the ratio
    kuzel Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
  4. EQL triangle
    rs_triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
  5. Block
    brick_lego Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
  6. Vector
    some_vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
  7. Euklid4
    euclid_2 Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
  8. XY triangle
    triangle Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
  9. Shooter
    terc_1 The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?
  10. Slope of the pool
    swimming_pool Calculate slope (rise:run) of the bottom of swimming pool long 10 m. Water depth at beginning of pool is 1.16 m (for children) and depth at end is 1.89 m (for swimmers). Slope express as percentage and as angle in degrees.
  11. Nine-gon
    9gon_1 Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
  12. Sphere and cone
    cone_in_sphere Within the sphere of radius G = 36 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
  13. Road
    route-66 Average climb of the road is given by ratio 1:15. By what angle road average climb?
  14. Hexagonal prism
    hexa_prism The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
  15. Height difference
    road What height difference overcome if we pass road 1 km long with a pitch21 per mille?
  16. Elevation
    horizon_diagram What must be the elevation of an observer in order that he may be able to see an object on the earth 782 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
  17. Triangle and its heights
    triangle_2 Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
  18. Sea
    ship How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km).
  19. Euclid2
    euclid In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
  20. Triangular prism
    hranol_3sides The base perpendicular triangular prism is a right triangle whose hypotenuse measures 5 cm and one cathetus 2 cm. Height of the prism is equal to 7/9 of the perimeter of the base. Calculate the surface area of prism.

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