Tangent + triangle - math problems

Tangent is a trigonometric function. In a rectangular triangle, it is the ratio of the opposite and adjacent side to a given internal angle. Algebraically is defined as the ratio of the sine and cosine of a given angle. It is periodic with a period of π = 180 °.

  1. Depth angles
    hrad At the top of the mountain stands a castle, which has a tower 30 meters high. We see the crossroad in the valley from the top of the tower and heel at depth angles of 32° 50 'and 30° 10'. How high is the top of the mountain above the crossroad
  2. Trapezoid MO
    right_trapezium The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
  3. Trigonometric functions
    trigonom In right triangle is: ? Determine the value of s and c: ? ?
  4. River
    river From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.
  5. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 7 cm.
  6. Cone
    cone-blue Calculate volume and surface area of ​​the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°.
  7. Rectangle
    golden-rectangle-ratio Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
  8. Climb
    Mazda_RX7_1 On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went?
  9. Triangular prism
    TriangularPrism Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.
  10. Regular quadrangular pyramid
    6 How many square meters is needed to cover the tower the shape of regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane is 68 °? Calculate coverage waste 10%.
  11. Road
    cesta Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B.
  12. Pyramid - angle
    pyramid Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees.
  13. 4side pyramid
    ihlany Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
  14. n-gon II
    x-gon_1 What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
  15. Stairway
    steps What angle rising stairway if step height in 17 cm and width 27 cm?
  16. Climb
    scenic_road Road has climbing 1:27. How big is a angle corresponds to this climbing?
  17. Tetrahedral pyramid
    pyramid_4s Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
  18. Steeple
    church_tower Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?
  19. Two forces
    vector-add Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
  20. V-belt
    v_belt Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.

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