The Law of Cosines - math word problems

  1. The spacecraft
    Sputnik_670 The spacecraft spotted a radar device at altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered
  2. Circular railway
    described_circle2 The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
  3. A rhombus
    rhombus-diagonals2 A rhombus has sides of length 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus.
  4. Children playground
    lich_5 The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.
  5. Calculate 2
    t_sss Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm
  6. 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?
  7. Largest angle of the triangle
    obtuse_triangle Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
  8. ABCD
    trig_1 AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
  9. 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.
  10. 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).
  11. 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.
  12. 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.
  13. 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?
  14. 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?
  15. Diagonals in diamond
    diagonalsf In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
  16. Scalene triangle
    triangles_1 Solve the triangle: A = 50°, b = 13, c = 6
  17. 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
  18. Vector sum
    vectors 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?
  19. Diagonals
    diagonals Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
  20. Greatest angle
    triangles_4 Calculate the greatest triangle angle with sides 197, 208, 299.

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Cosine rule uses trigonometric SAS triangle calculator.