The Law of Cosines - practice problems - page 2 of 5
Instructions: For each problem, solve carefully and show your complete working.Number of problems found: 85
- Triangle from median
Calculate the perimeter, area, and magnitudes of the triangle ABC's remaining angles: a = 8.4; β = 105° 35 '; and median ta = 12.5. - Triangle and its heights
Calculate the length of the sides of the triangle ABC if va=13 cm, vb=15 cm and side b are 5 cm shorter than side a. - 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? - Largest angle of the triangle
Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - Medians of isosceles triangle
The isosceles triangle has a base ABC |AB| = 16 cm and a 10 cm long arm. What is the length of the medians? - Sides ratio and angles
In triangle ABC, you know the ratio of side lengths a:b:c=3:4:6. Calculate the angle sizes of triangle ABC. - SAS calculation
Given the triangle ABC, if side b is 31 ft., side c is 22 ft., and angle α is 47°, find side a. Please round to one decimal. - Triangle 75
Triangle ABC has angle C bisected and intersected AB at D. Angle A measures 20 degrees, and angle B measures 40 degrees. The question is to determine AB-AC if length AD=1. - Parallelogram - angle alfa
In the parallelogram ABCD the length of sides are AB = 8, BC = 5, BD = 7. Calculate the magnitude of the angle α = ∠DAB (in degrees). - ABCD
AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD - 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. - Triangle sides to angles
The triangle ABC has side lengths a = 14 cm, b = 20 cm, c = 7.5 cm. Find the sizes of the angles and the area of this triangle. - 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. - 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? - Diagonals in diamond
In the rhombus, a = 160 cm and alpha = 60 degrees are given. Calculate the length of the diagonals. - Diagonals
Calculate the length of the rhombus's diagonals if its side is long 21 and one of its internal angles is 10°. - On a mass
The forces F1, and F2 with magnitudes of 40N act on a mass point M. Their resultant has a magnitude of 60N. Determine the angle that the forces F1 and F2 make. - 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. - 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 - Rhombus - diagonals
Rhombus ABCD has side a = 80 cm and side b = 50 cm. Diagonals u1 and u2 make an angle of 60 degrees with each other. Calculate the area of the rhombus.
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