# The Law of Cosines - math word problems

#### Number of problems found: 36

• 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.
• 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?
• 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 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?
• 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.
• Calculate 2
Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm
• 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
Plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3] give Triangle KLM. Calculate its area and its interior angles.
• 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.
• 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?
• Distance of points
A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S.
• 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.
• 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.
• Triangle SAS
Calculate the triangle area and perimeter, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
• The spacecraft
The spacecraft spotted a radar device at altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered a