# Triangle + The Law of Cosines - math problems

- Circular railway

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? - A rhombus

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. - Triangle SAS

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 °. - Triangle

Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and itsinterior angles. - 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 - ABCD

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

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Cosine rule uses trigonometric SAS triangle calculator. See also our trigonometric triangle calculator. See also more information on Wikipedia.