Goniomentry and trigonometry - math word problems

  1. Diagonal
    rectangles2 Diagonal of the rectangle has length 46.4 cm. Angle between diagonal and londer sife of rectangle is 22°. Calculate area of the rectangle.
  2. Block
    brick_lego Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
  3. Cone
    cone-blue Calculate volume and surface area of ​​the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.
  4. 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°?
  5. Gon functions
    quadrants Decide which of the numbers (values ​​of trigonometric functions) are positive and which are negative (or zero). Positive mark +1 and negative -1.
  6. Triangle
    star Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
  7. Greatest angle
    triangles_4 Calculate the greatest triangle angle with sides 197, 208, 299.
  8. Q-Exam
    unit_circle If tg α = 0.9, Calculating sin α, cos α, cotg α .
  9. Road
    route-66 Average climb of the road is given by ratio 1:15. By what angle road average climb?
  10. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and its interior angles.
  11. SAS triangle
    triangles2 The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle.
  12. Sines
    sines In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
  13. 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?
  14. Aircraft
    aircraft The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.
  15. Reflector
    lamp Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
  16. Parallelogram
    paralleogram Calculate area of the parallelogram ABCD as shown if |AB| = 19 cm, |BC| = 18 cm and angle BAD = 90°
  17. Side c
    trig-cos-law In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
  18. Two boats
    ship_1 Two boats are located from a height of 150m above the surface of the lake at depth angles of 57° and 39°. Find the distance of both boats if the sighting device and both ships are in a plane perpendicular to the surface of the lake.
  19. Stairway
    steps What angle rising stairway if step height in 17 cm and width 27 cm?
  20. Observer
    ohrada The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 102 m. How far is it from the another end of the fence?

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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.