# Cosine + The Law of Cosines - math problems

#### Number of problems found: 27

• 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?
• 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 ’?
• 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.
• Children playground The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine 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?
• 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.
• Diagonals in diamond In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
• 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
• 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?
• Diagonals Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
• Triangle Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and its interior angles.
• Greatest angle Calculate the greatest triangle angle with sides 197, 208, 299.
• Two boats Two boats are located from a height of 150m above the surface of the lake 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 surface of the lake.
• 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 va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
• 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 from median Calculate the perimeter, content, and magnitudes of the remaining angles of triangle ABC, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
• Scalene triangle Solve the triangle: A = 50°, b = 13, c = 6

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...

Cosine rule uses trigonometric SAS triangle calculator.