The Law of Cosines - practice problems - page 2 of 5
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 83
- Diagonals
Calculate the length of the rhombus's diagonals if its side is long 21 and one of its internal angles is 10°. - 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. - 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. - 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). - 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 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. - ABCD
AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD - 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. - 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. - Heptagon perimeter
Calculate a regular heptagon's perimeter if its shortest diagonal length is u=14.5cm. - Observation angle At what angle of view does an object 70 m long appear to the observer, 50 m away from one end and 80 m from the other end?
- Isosceles 7929
ABCD isosceles trapezoid. A = 6cm, e = 7cm and delta angle = 105 °. Calculate the remaining pages. - 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. - Circumscribed circle
In triangle ABC, we know a = 4 cm, b = 6 cm, γ = 60°. Calculate the area and radius of the inscribed and circumscribed circle. - A rhombus
A rhombus has sides of the length of 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus. - Cosine
Cosine and sine theorem: Calculate all unknown values (side lengths or angles) from triangle ABC. c = 2.9 cm; β = 28°; γ = 14° α =? °; a =? cm; b =? cm - Cosine
Cosine and sine theorem: Calculate all unknown values (sides and angles) of the triangle ABC. a = 20 cm; b = 15 cm; γ = 90°; c =? cm; α =? °; β =? ° - Circumscribed circle ABC
Triangle ABC, with sides a = 15 cm, b = 17.4 cm, and c = 21.6 cm, is circumscribed by a circle. Calculate the area of the segments determined by the sides of the triangle. - 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 the point S is the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side t - 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?
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