# Cosine + The Law of Cosines - math problems

#### Number of examples found: 25

- 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 remaining angles of triangle ABC, 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 ’? - 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 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? - 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. - 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 so that they are in balance. Determine the angles of the 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 - 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°. - Greatest angle

Calculate the greatest triangle angle with sides 197, 208, 299.

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