# The Law of Cosines - practice problems - page 2 of 3

#### Number of problems found: 58

- The angle of view

Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other. - Two groves

Two groves A, B are separated by a forest, both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B, if AC = 5004 m, BC = 2600 m and angle ABC = 53° 45 ’? - Circular railway

The railway connects 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. - Isosceles 7929

ABCD isosceles trapezoid. A = 6cm, e = 7cm and delta angle = 105 °. Calculate the remaining pages. - Parallelogram

The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - Children playground

The playground has a trapezoid shape, and the parallel sides have a length of 36 m and 21 m. The remaining two sides are 14 m long and 16 m long. Find the size of the inner trapezoid angles. - Calculate 2

Calculate the largest angle of the triangle whose sides are 5.2cm, 3.6cm, and 2.1cm - 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? - Largest angle of the triangle

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

AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD - 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. - Parallelogram 5027

Calculate the area of the parallelogram if the side sizes are a = 80, b = 60, and the size of the diagonal angle is 60°. - 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. - Triangle 2668

The triangle ABC has side lengths a = 14 cm, b = 20 cm, c = 7.5 cm. Find the sizes of the angles and the area of this triangle. - Medians of isosceles triangle

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

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

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

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