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Explain the cosine rule and sine rule while also saying how to use it and provide examples (keep it in simple terms)

User Vrtis
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1 vote

Answer:

Explanation:

User Abdus Salam Azad
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Answer:

Sure, I'll explain the cosine rule and sine rule in simple terms:

The cosine rule (also known as the law of cosines) is used to find the length of a side or the measure of an angle in a triangle given the lengths of the other sides and the angle between those sides. It states that c^2 = a^2 + b^2 - 2ab cos(C), where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

Here's an example of how to use the cosine

Suppose we have a triangle with sides a=6, b=8, and an angle between them c=45 degrees. We want to find the length of the remaining side of the triangle, side a.

Using the cosine rule:

a^2 = b^2 + c^2 - 2bc * cosA

where A is the angle opposite side a, we can plug in our values and solve for a:

a^2 = 8^2 + 6^2 - 2(8)(6) * cos(45)

a^2 = 64 + 36 - 96 * 0.707

a^2 = 10.56

a = sqrt(10.56)

a = 3.25 (rounded to two decimal places)

Therefore, the length of side a is approximately 3.25 units.

User Heartless Vayne
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