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Trig - Cosine Rule watch

1. Please can somebody go set by step how to work out these questions only using the cosine rule.

thanks Sam
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2. What do you know so far? What have you done so far?
3. (Original post by berwick53)
Please can somebody go set by step how to work out these questions only using the cosine rule.

thanks Sam
The last time i did the cosine rule was like 8 months ago, but for a side it is =

C^2= A^2+B^2-2BA*COSc,

where c is your unknown, a and b are your known sides, and cos c is your angle opposite the unidentified side, so plug values in and square root to find c, there is a similar formula for the angle just plug values in
4. First one will be x^2 = 6^2+4^2-2 x 6 x 4 x cos47

Second one will be 3.5^2 = 4^2 + 5^2 - 2 x 4 x 5 x cosθ and rearrrange to get θ.
5. The cosine rule states that , where a is the length opposite the angle A, and b and c are the other two sides.

Cosine rule problems normally come in two forms:
#1: You know three side lengths and you need to find an angle
#2: You know an angle and two side lengths and you need to find the third side length

I'll tackle these two cases separately. [You have one of each to do in your problem set.]

Case #1 (Finding the angle given three side lengths):
Call the angle you're trying to find (capital), and label the side of the triangle which is opposite the angle (lower case). Then label the other two sides and (it doesn't matter which is which). Then substitute the values of into the equation, and solve the equation for by rearranging.

Case #2 (Finding a side lengths given an angle and two other side lengths):
Like in Case 1, call the angle you know , call the opposite side , and call the other two sides and (it doesn't matter which). Then you need to decide which of you're trying to find -- you know two of them, and you want to find the third. Pick out the one you're trying to find and substitute all the other values into the equation. You'll be left with something where the only letter (apart from 'cos') in the equation is the letter of the side you're trying to find the length of. You then just solve for this, again by rearranging.

If you need any more help, show us your working.
6. Sorted
7. (Original post by nuodai)
The cosine rule states that , where a is the length opposite the angle A, and b and c are the other two sides.

Cosine rule problems normally come in two forms:
#1: You know three side lengths and you need to find an angle
#2: You know an angle and two side lengths and you need to find the third side length

I'll tackle these two cases separately. [You have one of each to do in your problem set.]

Case #1 (Finding the angle given three side lengths):
Call the angle you're trying to find (capital), and label the side of the triangle which is opposite the angle (lower case). Then label the other two sides and (it doesn't matter which is which). Then substitute the values of into the equation, and solve the equation for by rearranging.

Case #2 (Finding a side lengths given an angle and two other side lengths):
Like in Case 1, call the angle you know , call the opposite side , and call the other two sides and (it doesn't matter which). Then you need to decide which of you're trying to find -- you know two of them, and you want to find the third. Pick out the one you're trying to find and substitute all the other values into the equation. You'll be left with something where the only letter (apart from 'cos') in the equation is the letter of the side you're trying to find the length of. You then just solve for this, again by rearranging.

If you need any more help, show us your working.
thanks i've worked out the length now i need to work out the angle. the calcuations I've done so far are:

12.25=41-40cosθ
40cosθ=28.75
cosθ=0.71875

I dont't have a clue if what I've done is correct and if it is what to do next.

Sam
8. (Original post by berwick53)
thanks i've worked out the length now i need to work out the angle. the calcuations I've done so far are:

12.25=41-40cosθ
40cosθ=28.75
cosθ=0.71875

I dont't have a clue if what I've done is correct and if it is what to do next.

Sam
This is almost right, except the bits I put in red should be negative (you rearranged the equation slightly wrong, but the numbers are right). Next you take the inverse cosine to find . That is, .

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Updated: September 29, 2010
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