The Law of Cosines - math problems

Number of problems found: 42

  • Four sides of trapezoid
    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.
  • Medians of isosceles triangle
    The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What is the length of medians?
  • Triangle ABC
    Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled?
  • Diagonals in diamond
    In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
  • Scalene triangle
    Solve the triangle: A = 50°, b = 13, c = 6
  • Find the area
    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
  • Diagonals
    Calculate the length of the rhombus's diagonals if its side is long 5 and one of its internal angles is 80°.
  • Greatest angle
    Calculate the greatest triangle angle with sides 197, 208, 299.
  • Two boats
    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.
  • Side c
    In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
  • Triangle and its heights
    Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
  • Laws
    From which law follows directly the validity of Pythagoras' theorem in the right triangle? ...
  • Heron backlaw
    Calculate missing side in a triangle with sides 25 and 13 and area 152.
  • Triangle SAS
    Calculate the triangle area and perimeter, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
  • Mass point
    Two equal forces of 30 Newtons act on a mass point. Find the magnitude of the resultant force if these forces form an angle of 42°.
  • Space vectors 3D
    The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, the distance between the vectors.
  • Triangle
    Plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3] give Triangle KLM. Calculate its area and its interior angles.
  • Vector sum
    The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
  • Three vectors
    The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point to balance. Determine the angles of each two forces.
  • Quadrilateral oblique prism
    What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°.

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Cosine rule uses trigonometric SAS triangle calculator.