What type of triangles use Law of Cosines and Sines
In a right triangle, we can find the unknown sides or angles using the Pythagorean Theorem. But if the given triangle is not right triangle and is an oblique triangle then how do we go about? In such triangles we use the Law of Cosines and Sines to solve triangles. Sine and Cosine Laws are given as follows: Law of Sines: a/Sin(A)=b/Sin(B)=c/Sin(C)
Law of Cosines: a^2=b^2+c^2-2bc Cos A; b^2=c^2+a^2-2ca Cos B ; c^2=a^2+b^2-2ab Cos C
In a given oblique triangle, when do we use Law of Sines and Law of Cosines
The Law of Sines are used when we know two sides and one opposite side or when we know two angles and one opposite side of an oblique triangle. The Law of Cosines are used when we know two sides and the included angle or given the three sides of an oblique triangle.
Law of Sines and Cosines
The Law of Sines help to establish a relationship between the side lengths and angles of a triangle ABC. There are three Sines and hence the relationship explains the plural ‘s’ of Law of Sines.
The Law of Sines are, a/Sin[A] = b/Sin[B] =c/Sin[C] or we can even write them as Sin[A]/a=Sin[B]/b=Sin[C]/c ; where a,b,c are the side lengths and A, B and C are the opposite angles of the respective sides a,b,c in the oblique triangle ABC
The Law of Cosines is used most widely than the Law of Sines. When we know two sides of a triangle and their included angle, then Law of Cosines enables us to find the third side. The plural‘s’ in the law of Cosines is used as there are three cosines and hence by rotation similar formulas are valid for other angles. Law of Cosines are, a^2=b^2+c^2-2bc Cos A; b^2=c^2+a^2-2ca Cos B ; c^2=a^2+b^2-2ab Cos C. The Law of Sines and Cosines, are also known as the Sine Rule and the Cosine Rule.
Solving Law of Sines and Cosines Word Problems
Let us solve some Law of Sines and Cosines Problems with the given side lengths and angles
Example: Peter wants to measure the height of a tree. He walks 100ft from the base of the tree and looks up. The angle of elevation found is 33 degrees. This particular tree grows at an angle of 83 degrees with respect to the ground rather than vertically. Calculate the height of the tree.
Solution:
Angle B=83 degrees , Angle A= 33 degrees, c=100ft [two angles and included side]
Angle C= 180-[angle A+angleB] = 180-116= 64 degrees
Using Sine Rule, a/SinA = c/SinC
a = c . SinA/SinC = 100. Sin(33)/Sin(64) = 100. (0.606) = 60.6
So, the height of the tree calculated by Peter is 60.6 ft
Know more about the Math Homework Help,online Math help. This article gives basic information about Standard deviation. Next article will cover more statistics concept and its advantages,problems and many more. Please share your comments.
In a right triangle, we can find the unknown sides or angles using the Pythagorean Theorem. But if the given triangle is not right triangle and is an oblique triangle then how do we go about? In such triangles we use the Law of Cosines and Sines to solve triangles. Sine and Cosine Laws are given as follows: Law of Sines: a/Sin(A)=b/Sin(B)=c/Sin(C)
Law of Cosines: a^2=b^2+c^2-2bc Cos A; b^2=c^2+a^2-2ca Cos B ; c^2=a^2+b^2-2ab Cos C
In a given oblique triangle, when do we use Law of Sines and Law of Cosines
The Law of Sines are used when we know two sides and one opposite side or when we know two angles and one opposite side of an oblique triangle. The Law of Cosines are used when we know two sides and the included angle or given the three sides of an oblique triangle.
Law of Sines and Cosines
The Law of Sines help to establish a relationship between the side lengths and angles of a triangle ABC. There are three Sines and hence the relationship explains the plural ‘s’ of Law of Sines.
The Law of Sines are, a/Sin[A] = b/Sin[B] =c/Sin[C] or we can even write them as Sin[A]/a=Sin[B]/b=Sin[C]/c ; where a,b,c are the side lengths and A, B and C are the opposite angles of the respective sides a,b,c in the oblique triangle ABC
The Law of Cosines is used most widely than the Law of Sines. When we know two sides of a triangle and their included angle, then Law of Cosines enables us to find the third side. The plural‘s’ in the law of Cosines is used as there are three cosines and hence by rotation similar formulas are valid for other angles. Law of Cosines are, a^2=b^2+c^2-2bc Cos A; b^2=c^2+a^2-2ca Cos B ; c^2=a^2+b^2-2ab Cos C. The Law of Sines and Cosines, are also known as the Sine Rule and the Cosine Rule.
Solving Law of Sines and Cosines Word Problems
Let us solve some Law of Sines and Cosines Problems with the given side lengths and angles
Example: Peter wants to measure the height of a tree. He walks 100ft from the base of the tree and looks up. The angle of elevation found is 33 degrees. This particular tree grows at an angle of 83 degrees with respect to the ground rather than vertically. Calculate the height of the tree.
Solution:
Angle B=83 degrees , Angle A= 33 degrees, c=100ft [two angles and included side]
Angle C= 180-[angle A+angleB] = 180-116= 64 degrees
Using Sine Rule, a/SinA = c/SinC
a = c . SinA/SinC = 100. Sin(33)/Sin(64) = 100. (0.606) = 60.6
So, the height of the tree calculated by Peter is 60.6 ft
Know more about the Math Homework Help,online Math help. This article gives basic information about Standard deviation. Next article will cover more statistics concept and its advantages,problems and many more. Please share your comments.
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