Law of cosines - examples

Cosine rule uses trigonometric SAS triangle calculator.

  1. Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  2. Side c
    trig-cos-law In △ABC a=3, b=8 and ∠C=70°. Calculate length of the side c.
  3. Heron backlaw
    heron_math Calculate missing side in a triangle with sides 33 and 27 and area 118.3.
  4. Triangle SAS
    triangle_iron Calculate area and perimeter of the triangle, if the two sides are 19 cm and 80 cm long and angle them clamped is 90°.
  5. Greatest angle
    triangles_4 Calculate the greatest triangle angle with sides 464, 447, 274.
  6. Find the area
    triangles_57 Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft
  7. Vector sum
    vectors The magnitude of the vector u is 8 and the magnitude of the vector v is 11. Angle between vectors is 65°. What is the magnitude of the vector u + v?
  8. Diagonals in diamond
    diagonalsf In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
  9. Triangle ABC
    squares4 Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled?
  10. Diagonals
    diagonals Calculate the length of the diagonals of the rhombus if its side is long 27 and one of its internal angle is 70°.
  11. Triangle and its heights
    triangle_2 Calculate the length of the sides of the triangle ABC, if va=13 cm, vb=17 cm and side b is 5 cm shorter than side a.
  12. Scalene triangle
    triangles_1 Solve the triangle: A = 50°, b = 13, c = 6

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