In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles. According to the law,
a
sin
A
=
b
sin
B
=
c
sin
C
=
2
R
,
{\displaystyle {\frac {a}{\sin A}}\,=\,{\frac {b}{\sin B}}\,=\,{\frac {c}{\sin C}}\,=\,2R,}
where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles (see the figure to the right), while R is the radius of the triangle's circumcircle. When the last part of the equation is not used, the law is sometimes stated using the reciprocals;
sin
A
a
=
sin
B
b
=
sin
C
c
.
{\displaystyle {\frac {\sin A}{a}}\,=\,{\frac {\sin B}{b}}\,=\,{\frac {\sin C}{c}}.}
The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known—a technique known as triangulation. It can also be used when two sides and one of the non-enclosed angles are known. In some such cases, the triangle is not uniquely determined by this data (called the ambiguous case) and the technique gives two possible values for the enclosed angle.
The law of sines is one of two trigonometric equations commonly applied to find lengths and angles in scalene triangles, with the other being the law of cosines.
The law of sines can be generalized to higher dimensions on surfaces with constant curvature.
Homework Statement
Given is a triangle with sides a=3.1cm, b=5cm, c=4.7cm and opposite angle to side a, α=36°. I must find out for angles β and γ using the law of sines.
Homework Equations
Law of sines.
The Attempt at a Solution
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I first tried:
sin(γ)}/c=sin(α)/a ⇒ γ≈63.02°...
Homework Statement
Hi, I'm having trouble with my first mechanics assignment and I'd appreciate some help.
So, an object is being pulled using two ropes (Fa and Fb) with a resultant force of 970 N along the x axis. Angle from Fa to the axis is 20 degrees, angle from fb to the axis is 51...
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Thread
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mechanics
physics
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statics
Homework Statement
Hello!
Please, help me to understand the task - I seem to fail to understand what goes where, and hence cannot proceed to solving the exercise. Please, take a look at the task, and then my questions. The task is on using the law of sines. Before trying to solve it I need to...
I am trying to derive the law of signs from the cross product.
First, we have three vectors ##\vec{A} ~\vec{B} ~\vec{C}## such that ##\vec{A} + \vec{B} + \vec{C} = 0##. This creates a triangle. Then, we label the angles opposite the respective sides as a, b, and c. I am not sure where to go...
Homework Statement
A model for the suspension of a vehicle is shown where the spring has stiffness k = 178 N.mm and an unstretched length of 347 mm.
Here is the picture: http://i.imgur.com/1dTVs12.jpg
Part a asked to determine the value of P and the force supported by member AB so that the...
Homework Statement
Homework Equations
SinA/a = SinB/b = SinC/c
The Attempt at a Solution
a=38, c=44, ∠A = 35°
What I have so far:
sin(35)/38 = sinC/44
44sin(35) = 38sinC
44sin(35)/38 = sinC
sinC = 0.6641
sin^-1(0.6641)
∠C = 41.6º
Is this ∠C1?
After this I don't know how to...