The Law of Cosines - practice problems
The law of cosines is a mathematical formula used in trigonometry that relates the sides of a triangle to the cosine of one of its angles. Specifically, it states that in any triangle with sides a, b, and c and angles A, B, and C opposite to those sides, the following equation holds:c2 = a2 + b2 - 2ab * cos(C)
where c is the length of the side opposite angle C, a is the length of the side opposite angle A, and b is the length of the side opposite angle B. The formula is also known as "cosine formula" or "cosine rule".
The law of cosines can be used to find the length of a side of a triangle when the lengths of the other two sides and the angle opposite the unknown side are known. It can also be used to find an angle of a triangle when the lengths of all three sides are known.
It is particularly useful in solving triangles that are not right triangles, where the Pythagorean theorem can not be applied.
The law of cosines can also be useful in solving problems involving distance and navigation, like finding the distance between two points on the surface of the earth, or finding the distance between two celestial bodies. It is also used in physics and engineering, such as in calculating the force required to bend a beam of a certain length and material properties.
Direction: Solve each problem carefully and show your solution in each item.
Number of problems found: 83
- Cosine - legs
Using the law of cosines, find the measurement of leg b if the givens are β=20°, a=10, and c=15. - Rhombus 36
Rhombus ABCD with side 8 cm long has diagonal BD 11.3 cm long. Find angle DAB. - A triangle 7
A triangle lot has the dimensions a=15m, b=10m, and c=20m. What is the measure of the angle between the sides of b and c? - Three 235
Three houses form a triangular shape. House A is 50 feet from house C and house B is 60 feet from house C. The measure is angle ABC is 80 degrees. Draw a picture and find the distance between A and B. - Piece of a wire
A piece of wire is bent into the shape of a triangle. Two sides have lengths of 24 inches and 21 inches. The angle between these two sides is 55°. What is the length of the third side to the nearest hundredth of an inch? A: The length of the third side is - Triangle 90
Triangle made by 6 cm 4.5 cm and 7.5 cm. what angles does it make? - Laws
From which law directly follows the validity of Pythagoras' theorem in the right triangle? ...
- Scalene triangle
Solve the triangle: A = 50°, b = 13, c = 6 - Isosceles triangle and cosine
Using the cosine theorem, prove that in an isosceles triangle ABC with base AB, c=2a cos α. - Big tower
From a tower 15 meters high and 30 meters away from the river, the width of the river appeared at an angle of 15°. How wide is the river in this place? - 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. - 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. - Two forces 3
Two forces with magnitudes 8 Newtons and 15 Newtons act at a point. Find the angle between the forces if the resultant force is 17 Newtons. - Parallelogram 65954
In the parallelogram ABCD AB = 8, BC = 5, BD = 7. Calculate the magnitude of the angle α = ∠DAB (in degrees). - 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. - 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. - Triangle ABC
Triangle ABC has side lengths m-1, m-2, and m-3. What has to be m to be a triangle a) rectangular b) acute-angled? - Side c
In △ABC a=1, b=6 and ∠C=110°. Calculate the length of the side c. - Observer 64354
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?
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Cosine rule uses trigonometric SAS triangle calculator.
