# Law of cosines - examples

- Triangle SAS

Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°. - 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 17 and 34 and area 275. - 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 v_{a}=5 cm, v_{b}=7 cm and side b is 5 cm shorter than side a. - Diagonals

Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°. - Diagonals in diamond

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

Calculate the greatest triangle angle with sides 197, 208, 299. - 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? - 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. - 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. - 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). - 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. - Medians of isosceles triangle

The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians? - 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 - ABCD

AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD - Largest angle of the triangle

Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - The pond

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?

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Cosine rule uses trigonometric SAS triangle calculator.