# Law of cosines - math word problems

1. 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 °.
2. Laws
From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
3. Heron backlaw
Calculate missing side in a triangle with sides 17 and 34 and area 275.
4. Side c
In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
5. 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.
6. Diagonals
Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
7. Diagonals in diamond
In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
8. 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?
9. Greatest angle
Calculate the greatest triangle angle with sides 197, 208, 299.
10. Triangle ABC
Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled?
11. 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.
12. 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.
13. Angles by cosine law
Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
14. 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.
15. Medians of isosceles triangle
The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians?
16. Scalene triangle
Solve the triangle: A = 50°, b = 13, c = 6
17. 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
18. ABCD
AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
19. Largest angle of the triangle
Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
20. 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?

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Cosine rule uses trigonometric SAS triangle calculator.