# Law of cosines - examples

Cosine rule uses trigonometric SAS triangle calculator.- Inner angles

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. - Laws

From which law follows directly the validity of Pythagoras' theorem in the right triangle? ? - Side c

In △ABC a=3, b=8 and ∠C=70°. Calculate length of the side c. - Heron backlaw

Calculate missing side in a triangle with sides 33 and 27 and area 118.3. - Greatest angle

Calculate the greatest triangle angle with sides 464, 447, 274. - Triangle SAS

Calculate area and perimeter of the triangle, if the two sides are 19 cm and 80 cm long and angle them clamped is 90°. - 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 - Vector sum

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? - Diagonals in diamond

In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals. - 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

Calculate the length of the diagonals of the rhombus if its side is long 27 and one of its internal angle is 70°. - Triangle and its heights

Calculate the length of the sides of the triangle ABC, if v_{a}=13 cm, v_{b}=17 cm and side b is 5 cm shorter than side a. - Angles by cosine law

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). - 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. - Three vectors

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. - Scalene triangle

Solve the triangle: A = 50°, b = 13, c = 6

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