From the observatory 11 m high and 24 m from the riverbank, river width appears in the visual angle φ = 13°. Calculate the width of the river.

Correct result:

y =  29.5 m


h=11 m x=24 m A=13 rad=13 π180 =13 3.1415926180 =0.22689 rad B=arctan(x/h)=arctan(24/11)1.141 C=A+B=0.2269+1.1411.3679 rad c=180/π C=180/3.1416 1.367978.3764 tanC=(x+y)/h y=h tan(C)x=11 tan(1.3679)24=29.5 m

We would be pleased if you find an error in the word problem or inaccuracies and send it to us. Thank you!

Showing 0 comments:

Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Do you want to convert length units?
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions:

  • Right angle
    rt_triangle_1 In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
  • Tree
    strom How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground.
  • Right triangle trigonometrics
    triangle2 Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
  • Mast
    stoziar Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 13.3°. Determine the height of the mast, if the sun above the horizon is at angle 45°12'.
  • 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.
  • Stairway
    steps What angle rising stairway if step height in 20 cm and width 26 cm?
  • Water channel
    trapezium_prism_2 The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flo
  • Perimeter of triangle
    rt_triangle_1 In triangle ABC angle A is 60° angle B is 90° side size c is 15 cm. Calculate the triangle circumference.
  • TV tower
    Žižkov_tv_tower Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°?
  • Tower
    cone_roof How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°?
  • The mast
    geodet_1 The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole?
  • Two triangles SSA
    ssa Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
  • The staircase
    schody The staircase has a total height of 3.6 m and forms an angle of 26° with the horizontal. Calculate the length of the whole staircase.
  • Clouds
    uhly Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us?
  • Building
    Taipei_101 How high is the building that throws horizontal shadow 95.4 m long at angle 50°?
  • Slope of track
    sklon_1 Calculate the average slope (in permille and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitrianske Pravno (354 m AMSL), if the track is 11 km long.
  • Right triangle
    rt_A Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.