Observation tower

From the observation tower at a height of 105 m above sea level, the ship is aimed at a depth angle of 1° 49´. How far is the ship from the base of the tower?

Result

x =  198.695 km

Solution:

h=105 m A=1/60+49/3600=10936000.0303   tanA=h:x  x1=h/tanA=h/tan0.0302777777778 =105/tan0.0302777777778 =h/0.000528=198695.43706  x=x1km=x1/1000 km=198695.437063/1000 km=198.69544 km=198.695 kmh=105 \ \text{m} \ \\ A=1/60 + 49/3600=\dfrac{ 109 }{ 3600 } \doteq 0.0303 \ ^\circ \ \\ \ \\ \tan A=h:x \ \\ \ \\ x_{1}=h/\tan A ^\circ =h/\tan 0.0302777777778^\circ \ =105/\tan 0.0302777777778^\circ \ =h/0.000528=198695.43706 \ \\ \ \\ x=x_{1} \rightarrow km=x_{1} / 1000 \ km=198695.437063 / 1000 \ km=198.69544 \ km=198.695 \ \text{km}



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Do you want to convert length units?
See also our right triangle calculator.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  1. Lookout tower
    marhat Calculate the height of a lookout tower forming a shadow of 36 m if at the same time a column 2.5 m high has a shadow of 1.5 m.
  2. Side lengths
    triangles_1 In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.
  3. Interior angles
    triangles_1 Calculate the interior angles of a triangle that are in the ratio 2: 3: 4.
  4. The bases
    rr_lichobeznik The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid.
  5. The angles ratio
    123_triangle The angles in the ABC triangle are in the ratio 1: 2: 3. find the sizes of the angles and determine what kind of a triangle it is.
  6. The right triangle
    rt_tr540 The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. Calculate the length of the leg b and the median t2 to side b.
  7. Concentric circles and chord
    tetiva2 In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?
  8. In a
    triangles_1 In a triangle, the aspect ratio a: c is 3: 2 and a: b 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides.
  9. Annulus from triangle
    annulus2 Calculate the content of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm
  10. Triangular prism
    hranol3b_1 Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm.
  11. Cone roof
    kuzel2 How many m2 of roofing is needed to cover a cone-shaped roof with a diameter of 10 m and a height of 4 m? Add an extra 4% to the overlays.
  12. Flakes
    kvietok_MO A circle was described on the square, and a semicircle above each side of the square was described. This created 4 "flakes". Which is bigger: the content of the central square or the content of four chips?
  13. Interior angles
    circle_inscribed_polygon In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles.
  14. The angles
    trojuholnik The angles in the triangle are in the ratio 12: 15: 9. Find the angles.
  15. Probability
    fractions_1 How probable is a randomly selected three-digit number divisible by five or seven?
  16. The triangles
    triangle1 The triangles KLM and ABC are given, which are similar to each other. Calculate the lengths of the remaining sides of the triangle KLM, if the lengths of the sides are a = 7 b = 5.6 c = 4.9 k = 5
  17. The conical
    cone_1 The conical candle has a base diameter of 20 cm and a side of 30 cm. How much dm ^ 3 of wax was needed to make it?