Law of cosines - examples

Cosine rule uses trigonometric SAS triangle calculator.

  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. Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  3. Side c
    trig-cos-law In △ABC a=3, b=8 and ∠C=70°. Calculate length of the side c.
  4. Heron backlaw
    heron_math Calculate missing side in a triangle with sides 33 and 27 and area 118.3.
  5. Greatest angle
    triangles_4 Calculate the greatest triangle angle with sides 464, 447, 274.
  6. 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°.
  7. 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
  8. 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?
  9. Diagonals in diamond
    diagonalsf In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
  10. 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?
  11. 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°.
  12. 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.
  13. Angles by cosine law
    357_triangle Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
  14. 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.
  15. Three vectors
    vectors_sum0 The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
  16. Scalene triangle
    triangles_1 Solve the triangle: A = 50°, b = 13, c = 6

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