Cosine - examples

  1. Square pyramid
    pyramid_4 Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
  2. Angle of deviation
    kuzel2_1 The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
  3. Four sides of trapezoid
    lichobeznik-stredni_pricka_3 In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
  4. 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)
  5. Cosine
    cosine The point (21, 20) is on the terminal side of angle θ. cos θ = ?
  6. Side c
    trig-cos-law In △ABC a=3, b=8 and ∠C=70°. Calculate length of the side c.
  7. Trigonometric functions
    trigonom In right triangle is: ? Determine the value of s and c: ? ?
  8. 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?
  9. 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)
  10. 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).
  11. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 11 cm.
  12. 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?
  13. Trigonometry
    trigonometry If you know that cos(α) = sin (-968°), what is the angle α?
  14. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?
  15. 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?
  16. Earth parallel
    parallels Earth's radius is 6378 km long. Calculate the length parallel of latitude 50°.
  17. 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?
  18. 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.
  19. 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.
  20. 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.

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