Pythagorean theorem + The Law of Cosines - math problems

  1. The pond
    rybnik_3 We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
  2. 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).
  3. Medians of isosceles triangle
    iso1 The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians?
  4. 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?
  5. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and its interior angles.
  6. Triangle and its heights
    triangle_2 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.
  7. Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  8. Triangle SAS
    triangle_iron Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.

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Cosine rule uses trigonometric SAS triangle calculator. Pythagorean theorem is the base for the right triangle calculator.