Cosine + The Law of Cosines - practice problems - page 3 of 4
Number of problems found: 62
- Determine 8133
Determine the distance between two places, M, and N, between which there is an obstacle so that place N is not visible from place M. The angles MAN = 130°, NBM = 109°, and the distances |AM| = 54, |BM| = 60, while the points A, B, and M lie on one straigh - 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 of 65°37'. Its endpoints are 155 m and 177 m away from the observer. What is the width of the pond? - 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 shortest side length, and 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. - Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point to balance. Determine the angles of each two forces. - 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 - Measurements of a triangle
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 12 and the magnitude of the vector v is 8. The angle between vectors is 61°. What is the magnitude of the vector u + v? - Diagonals
Calculate the length of the rhombus's diagonals if its side is long 5 and one of its internal angles is 80°. - Triangle
Plane coordinates of vertices: K[19, -4] L[9, 13] M[-20, 8] give Triangle KLM. Calculate its area and its interior angles. - Greatest angle
Calculate the greatest triangle angle with sides 124, 323, 302. - Two boats
Two boats are located from a height of 150m above the lake's surface at depth angles of 57° and 39°. Find the distance of both boats if the sighting device and both ships are in a plane perpendicular to the lake's surface.
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