Goniomentry and trigonometry - math word problems

  1. Triangle and its heights
    triangle_2 Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
  2. Building
    Taipei_101 How high is the building that throws horizontal shadow 95.4 m long at angle 50°?
  3. Equilateral triangle
    3angle_in_circle How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it?
  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. Triangle in circle
    triangle_in_circle Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
  6. Slope
    slope What is the slope of a line with an inclination 6.06 rad?
  7. IS triangle
    isoscelestriangle-pic Calculate interior angles of the isosceles triangle with base 46 cm and legs 49 cm long.
  8. Rhombus
    rhombus2 Internal angles of rhombus is in ratio 2:3. How many times is the shorter diagonal longer than side of rhombus?
  9. Angles
    rhombus_1 Determine the interior angles of a rhombus with area 319.1 cm2 and perimeter 72 cm.
  10. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 7 cm.
  11. Earth's circumference
    parallels Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
  12. Rhomboid
    parallelogram Calculate the circumference and area of the rhomboid with sides 20 and 14, with their angle 50°.
  13. Cotangent
    sin_cos If the angle α is acute, and cotg α = 1/3. Determine the value of sin α, cos α, tg α.
  14. 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.
  15. Triangle TBC
    isosceles_triangle TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB?
  16. Diagonal
    krychle Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
  17. Right
    r_triangle_1 Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
  18. Forces
    ijk In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
  19. Climb
    scenic_road Road has climbing 1:27. How big is a angle corresponds to this climbing?
  20. Pentagon
    5gon_3 Calculate the area of regular pentagon, which diagonal is u=17.

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...



Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.