Cosine - examples

  1. Inner angles
    triangle_1111 The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
  2. Circular sector
    vysek_circle I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector?
  3. Angle between vectors
    arccos Find the angle between the given vectors to the nearest tenth of a degree. u = (24, -1) and v = (12, 16)
  4. Cosine
    cosine The point (21, 20) is on the terminal side of angle θ. cos θ = ?
  5. Side c
    trig-cos-law In △ABC a=3, b=8 and ∠C=70°. Calculate length of the side c.
  6. Trigonometric functions
    trigonom In right triangle is: ? Determine the value of s and c: ? ?
  7. Cuboid
    cuboid_3 Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees).
  8. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 11 cm.
  9. Triangle TBC
    isosceles_triangle TBC is isosceles triangle with base TB with base angle 52° and legs length |TC| = |BC| = 30. How long is the base TB?
  10. Steeple
    church_tower Steeple seen from the road at an angle of 57°. When we zoom out to 25 meters, it is seen at an angle of 21°. What is high?
  11. Trigonometry
    trigonometry If you know that cos(α) = sin (-968°), what is the angle α?
  12. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?
  13. House roof
    roof_pyramid_2 The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m2 is needed to cover roof if roof pitch is 52° and we calculate 9% of waste, connections and overlapping of area roof?
  14. Mast
    stoziar Mast has 9 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.8°. Determine the height of the mast, if the sun above the horizon is at angle 36°6'.
  15. Earth parallel
    parallels Earth's radius is 6378 km long. Calculate the length parallel of latitude 50°.
  16. Cosine
    theta Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 19 and 4 and with the hypotenuse 19.416.
  17. Felix
    astronaut Calculate how much land saw Felix Baumgartner after jump from 22 km above ground. The radius of the Earth is R = 6378 km.
  18. Rectangle
    golden-rectangle-ratio Calculate the length of the side FL and diagonal JL of rectangle JFLB when given: |BL| = 33 cm and angle ∠ JFB = 32 degrees.
  19. Building
    building The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
  20. Greatest angle
    triangles_4 Calculate the greatest triangle angle with sides 464, 447, 274.

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