Triangle - 9th grade (14y) - examples - page 6

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  1. Cathethus and the inscribed circle
    RightTriangleInradius In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
  2. Triangular prism
    hranol_3 Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.
  3. Circumferential angle
    uhly Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 5:5:3. Determine the size of the angles of the triangle ΔABC.
  4. Distance
    distance Calculate distance between two points Z[7; -9] and U[-10; -8].
  5. ISO trapezium
    trapezium_2 Calculate area of isosceles trapezoid with base 53 long, leg 43 long and with the angle between the base and leg 70 degrees.
  6. Height
    equilateral_triangle Calculate height of the equilateral triangle if its perimeter is 54?
  7. Map - climb
    Lanovka_na_skalnate_pleso On the map of High Tatras in scale 1:25000 are cable car stations in the Tatranska Lomnica and in the Skalnate Pleso with distance 156 mm. Altitude of this stations are 944 m and 1755 m. What is average angle of climb of this cable car track?
  8. Triangle TBC
    isosceles_triangle TBC is isosceles triangle with base TB with base angle 52° and legs length |TC| = |BC| = 30. How long is the base TB?
  9. Cable car 2
    lanovka_1 Cable car rises at an angle 39° and connects the upper and lower station with an altitude difference of 345 m. How long is the track of cable car?
  10. Circle
    talesova On the circle k with diameter |MN| = 41 J lies point J. Line |NJ|=12. Calculate the length of a segment JM.
  11. 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!
  12. Circles
    three-circles Three circles of radius 71 cm 76 cm and 22 cm is mutually tangent. What is the perimeter of the triangle whose vertices are centers of the circles?
  13. Aircraft
    aircraft The plane flies at altitude 6800 m. At the time of first measurement was to see the elevation angle of 20° and second measurement of the elevation angle of 34°. Calculate the distance the plane flew between the two measurements.
  14. Park
    park_voda In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
  15. Right triangle
    thales_2 Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.
  16. Hexagon 5
    hexagon_1 The distance of parallel sides of regular hexagonal is 81 cm. Calculate the length of the radius of the circle described to this hexagon.
  17. Isosceles trapezoid
    licho_1 Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm.
  18. Angles in a triangle
    fun The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=69°. What sizes have other angles in a triangle?
  19. Triangle SAA
    triangle_blue The triangle has one side long 34 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
  20. Railway
    train_1 Railway line had on 5.8 km segment climb 9 permille. How many meters track ascent?

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