Law of sines equation

What is the sine rule?

The Sine Rule The Law of Sines (sine rule) is an important rule relating the sides and angles of any triangle (it doesn’t have to be right-angled!): If a, b and c are the lengths of the sides opposite the angles A, B and C in a triangle, then: a = b = c. sinA sinB sinC.

What is the sine ratio formula?

The definition of the sine ratio is the ratio of the length of the opposite side divided by the length of the hypotenuse. Well, the length of the side opposite ∠C is the length of the hypotenuse, so sin ∠C = c/c = 1 Because ∠C is a right angle, m∠C = 90º, so sin 90º = 1.

What is the law of sines and cosines?

We saw in the section on oblique triangles that the law of cosines and the law of sines were useful in solving for parts of a triangle if certain other parts are known. That means the side a is opposite the angle A, the side b is opposite the angle B, and the side c is opposite the angle C.

How do you use sine?

In any right angled triangle, for any angle:The sine of the angle = the length of the opposite side. the length of the hypotenuse.The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.The tangent of the angle = the length of the opposite side. the length of the adjacent side.

What is cosine rule formula?

For any triangle: a, b and c are sides. C is the angle opposite side c. The Law of Cosines (also called the Cosine Rule) says: c2 = a2 + b2 − 2ab cos(C)

Why is sin less than 1?

the value of sin and Cos is always less than 1 because sin is equals two perpendicular ÷ hypotenuse and perpendicular is always smaller than hypotenuse so it is not possible that sin is greater than 1 same case in cos also cos is equals to base divided by hypotenuse and base is always smaller than hypotenuse so it is

Can Cos be more than 1?

Originally Answered: can the value of cosine be greater than 1? Yes, the value of cosine can be greater than one if and only if the the angle under consideration is complex. Thus it becomes evident that if u plug in i(root of -1) in the equation, you get approx 1.543 which is greater than one.

What is the ratio of tan?

The ratio of the adjacent side of a right triangle to the hypotenuse is called the cosine and given the symbol cos. cos = a / h. Finally, the ratio of the opposite side to the adjacent side is called the tangent and given the symbol tan. tan = o / a.

Where is angle of depression?

The angle of depression is the angle between the horizontal line of sight and the line of sight down to an object. For example, if you were standing on top of a hill or a building, looking down at an object, you could measure the angle of depression.

Who discovered the law of sines?

Joannes Von Muller

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What is sin a and sin B?

The sum formula works whether both angles are the same or different: sin(A + B) or sin(A + A). However, sin(A + A) is really sin 2A. So, sin 2A is sin A cos A + cos A sin A. They are both the same product, in opposite order, so this statement can be simplified to sin 2A = 2 sin A cos A.

How is law of cosine used in real life?

The law of cosines is used in the real world by surveyors to find the missing side of a triangle, where the other two sides are known and the angle opposite the unknown side is known. The law of cosines is also used whenever a triangle is involved.

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