Right triangle + The Law of Cosines - practice problems

Number of problems found: 42

Two forces 3
Two forces of magnitude 8 Newtons and 15 Newtons respectively act at a point. If the resultant force is 17 Newtons, find the angle between the forces.
Calculate triangle
In the triangle ABC, calculate the sizes of all heights, angles, perimeters and its area, if given a-40cm, b-57cm, c-59cm
The farmer
The farmer sees the back fence of the land, which is 50 m long at a viewing angle of 30 degrees. It is 92 m away from one end of the fence. How far is it from the other end of the fence?
Triangle's centroid
In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid) and point is S the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side to 2 d
Aircraft bearing
Two aircraft will depart from the airport simultaneously, the first with a course of 30° and the second with a course of 86°. Both fly at 330 km/h. How far apart will they be in 45 minutes of flight?
Two chords
From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.
Viewing angle
The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
Triangle from median
Calculate the perimeter, content, and magnitudes of the triangle ABC's remaining angles, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
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.
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 side 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.
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).

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See also our right triangle calculator. Cosine rule uses trigonometric SAS triangle calculator. Right triangle practice problems. The Law of Cosines - practice problems.