Sina sinb formula

This section looks at the Sine Law and Cosine Law. 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 If you wanted to find an angle, you can write this as: sinA = sinB = sinC a b c This video shows you how to use the Sine rule

June wants to measure the distance of one side of a lake. The lake can be expressed as the triangle ABC. Angle a is opposite side BC, angle b is opposite side AC, and angle c is opposite side AB. She knows angle a= 54 degrees and angle b= 43 degrees. She also knows side AC= 106 feet. What is the measure of side BC? It works either way! But I like to arrange it so that the unknown value is in the numerator of the fraction to the left of the equal sign. For example, if I don't know side b, I would write the equation like this: b / sinB = a / sinA Then it's really easy to rearrange the equation, plug in the values, and solve for b: b = (a ⋅ sinB) / sinA etc. If I didn't know ∠A, I would write (and rearrange) the equation like this: sinA / a = sinB / b sinA = (a ⋅ sinB) / b ∠A = sin⁻¹ [(a ⋅ sinB) / b] etc. Hope this helps! Hi,😄 *Let's make some recap first:-👍😁 You see, 180 degrees is the sum of all degrees together in triangles, and sine (sin) is a law of opposite/hypotenuse... and theta is a (greek) symbol used for unknown angle values,👍OK? Now that we recapped, let's answer ur question : *This video proofs that the law of sines is true, so basically, Sal is giving us this proof. Like any proof, we need to provide: example- different ways to solve that come with the same answer as the theory- and correct answer. Sal made a shortcut as proof. If you try with the calculator sine of any angle equals the same as subtracting the whole sum of angles from a given angle (variable or ...

I understand how this video proves the angle addition for sine, but not where this formula comes from to begin with, I feel like somewhere I missed a step. It seems like a very complex proof for such a simple concept, why can't we just add sine a + sine b directly? What is it about trig functions that makes angle additions so complicated? I felt like I was grasping all the trig identities/unit circle definitions, etc up to this point but just crashed & burned here... The video is very clear but it seems like there should be some sort of introductory video to the concept of adding angles & why we can't do it more easily... Maybe it's just me? This is a good question. Here's a proof I just came up with that the angle addition formula for sin() applies to angles in the second quadrant: Given: pi/2 < a < pi and pi/2 < b < pi // a and b are obtuse angles less than 180°. Define: c = a - pi/2 and d = b - pi/2 // c and d are acute angles. Theorem: sin(c + d) = sin(c)*cos(d) + cos(c)*sin(d) // angle addition formula for sin(). Substitute: sin((a - pi/2) + (b - pi/2)) = sin(a - pi/2)*cos(b - pi/2) + cos(a - pi/2)*sin(b - pi/2) Simplify: sin((a - pi/2) + (b - pi/2)) = sin(a + b - pi) sin(a + b - pi) = -sin(a + b) // from unit circle sin(a - pi/2) = -cos(a) and sin(b - pi/2) = -cos(b) // from unit circle cos(a - pi/2) = sin(a) and cos(b - pi/2) = sin(b) // from unit circle Substitute: -sin(a + b) = -cos(a)*sin(b) + sin(a)*(-cos(b)) Simplify and rearrange: sin(a + b) = sin(a)*cos(b) + ...

I understand how this video proves the angle addition for sine, but not where this formula comes from to begin with, I feel like somewhere I missed a step. It seems like a very complex proof for such a simple concept, why can't we just add sine a + sine b directly? What is it about trig functions that makes angle additions so complicated? I felt like I was grasping all the trig identities/unit circle definitions, etc up to this point but just crashed & burned here... The video is very clear but it seems like there should be some sort of introductory video to the concept of adding angles & why we can't do it more easily... Maybe it's just me? This is a good question. Here's a proof I just came up with that the angle addition formula for sin() applies to angles in the second quadrant: Given: pi/2 < a < pi and pi/2 < b < pi // a and b are obtuse angles less than 180°. Define: c = a - pi/2 and d = b - pi/2 // c and d are acute angles. Theorem: sin(c + d) = sin(c)*cos(d) + cos(c)*sin(d) // angle addition formula for sin(). Substitute: sin((a - pi/2) + (b - pi/2)) = sin(a - pi/2)*cos(b - pi/2) + cos(a - pi/2)*sin(b - pi/2) Simplify: sin((a - pi/2) + (b - pi/2)) = sin(a + b - pi) sin(a + b - pi) = -sin(a + b) // from unit circle sin(a - pi/2) = -cos(a) and sin(b - pi/2) = -cos(b) // from unit circle cos(a - pi/2) = sin(a) and cos(b - pi/2) = sin(b) // from unit circle Substitute: -sin(a + b) = -cos(a)*sin(b) + sin(a)*(-cos(b)) Simplify and rearrange: sin(a + b) = sin(a)*cos(b) + ...

This section looks at the Sine Law and Cosine Law. 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 If you wanted to find an angle, you can write this as: sinA = sinB = sinC a b c This video shows you how to use the Sine rule

June wants to measure the distance of one side of a lake. The lake can be expressed as the triangle ABC. Angle a is opposite side BC, angle b is opposite side AC, and angle c is opposite side AB. She knows angle a= 54 degrees and angle b= 43 degrees. She also knows side AC= 106 feet. What is the measure of side BC? It works either way! But I like to arrange it so that the unknown value is in the numerator of the fraction to the left of the equal sign. For example, if I don't know side b, I would write the equation like this: b / sinB = a / sinA Then it's really easy to rearrange the equation, plug in the values, and solve for b: b = (a ⋅ sinB) / sinA etc. If I didn't know ∠A, I would write (and rearrange) the equation like this: sinA / a = sinB / b sinA = (a ⋅ sinB) / b ∠A = sin⁻¹ [(a ⋅ sinB) / b] etc. Hope this helps! Hi,😄 *Let's make some recap first:-👍😁 You see, 180 degrees is the sum of all degrees together in triangles, and sine (sin) is a law of opposite/hypotenuse... and theta is a (greek) symbol used for unknown angle values,👍OK? Now that we recapped, let's answer ur question : *This video proofs that the law of sines is true, so basically, Sal is giving us this proof. Like any proof, we need to provide: example- different ways to solve that come with the same answer as the theory- and correct answer. Sal made a shortcut as proof. If you try with the calculator sine of any angle equals the same as subtracting the whole sum of angles from a given angle (variable or ...