Length + 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. A cell tower
    tower A cell tower is located at coordinates (-5, -7) and has a circular range of 12 units. If Mr. XYZ is located at coordinates (4,5), will he be able to get a signal?
  3. Two chords
    twochords In a circle with radius r = 26 cm two parallel chords are drawn. One chord has a length t1 = 48 cm and the second has a length t2 = 20 cm, with the center lying between them. Calculate the distance of two chords.
  4. The quadrilateral pyramid
    jehlan_4b_obdelnik The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.
  5. A drone
    drone A flying drone aimed the area for an architect. He took off perpendicularly from point C to point D. He was at a height of 300 m above the plane of ABC. The drone from point D pointed at a BDC angle of 43°. Calculate the distance between points C and B in
  6. Possible lengths
    triangles Find the most possible lengths for the third side of a triangle with sides 20 and 18.
  7. Three parallels
    rs_triangle The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
  8. Land boundary
    rt_triangle The land has the shape of a right triangle. The hypotenuse has a length of 30m. The circumference of the land is 72 meters. What is the length of the remaining sides of the land boundary?
  9. 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.
  10. Two chords
    tetivy Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
  11. The Eiffel Tower
    Eiffel-Tower-Paris The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height.
  12. Three altitudes
    triangle_vysky A triangle with altitudes 4; 5 and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle.
  13. Medians 2:1
    taznice3 Median to side b (tb) in triangle ABC is 12 cm long. a. What is the distance of the center of gravity T from the vertex B? b, Find the distance between T and the side b.
  14. Lighthouse
    majak Marcel (point J) lies in the grass and sees the top of the tent (point T) and behind it the top of the lighthouse (P). | TT '| = 1.2m, | PP '| = 36m, | JT '| = 5m. Marcel lies 15 meters away from the sea (M). Calculate the lighthouse distance from the sea
  15. Cable car
    lano_3 Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m.
  16. Balloon and bridge
    hlbkovy_angle From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
  17. 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.
  18. Vertices of a right triangle
    right_triangle_5 Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
  19. Depth angle
    cliff From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?
  20. Spruce height
    stromcek_7 How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?

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