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secondary 3 | A Maths
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need help with this qn, pls explain too :)
Date Posted: 3 years ago
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We use the cosine rule, sine rule and area of triangle formula for this question.
Date Posted:
3 years ago
is the cosine rule the exact same one as sine rule?
sine rule is the one we did just now right
sine rule is the one we did just now right
i dont really understand part b and c
The one earlier is NOT the sine rule.
You have three formulae to learn.
First one is the area of triangle formula, 1/2 ab sin C.
Second one is the sine rule, a/sin A = b/sinB = C/sinC
Third one is the cosine rule, a2 = b2 + c2 - 2bc cos A
You have three formulae to learn.
First one is the area of triangle formula, 1/2 ab sin C.
Second one is the sine rule, a/sin A = b/sinB = C/sinC
Third one is the cosine rule, a2 = b2 + c2 - 2bc cos A
Means you have not learnt the cosine rule and the sine rule yet. I will next explain when to use each rule.
The cosine rule (the one I used in part b) is used in one of the following circumstances.
1. You wish to find a third length, given the two other lengths and the INCLUDED angle. With this, we plug into the formula a2 = b2 + c2 - 2bc cos A where a is the side directly opposite angle A. Then lengths b and c will have a sandwiched angle A in between them. Plug into the formula, and then from there we can obtain the third length a.
2. You wish to find one angle given all three sides of the triangle. We must let this angle to be calculated be the included angle. Then we put in the formula accordingly and solve for the angle.
1. You wish to find a third length, given the two other lengths and the INCLUDED angle. With this, we plug into the formula a2 = b2 + c2 - 2bc cos A where a is the side directly opposite angle A. Then lengths b and c will have a sandwiched angle A in between them. Plug into the formula, and then from there we can obtain the third length a.
2. You wish to find one angle given all three sides of the triangle. We must let this angle to be calculated be the included angle. Then we put in the formula accordingly and solve for the angle.
The sine rule (part c) is used in one of the following circumstances.
1. You are given two angles and a length, and you wish to find the value of a second length. With the two angles, you can easily work out the third angle. We link the known length with its opposite length and the unknown length to calculate with its opposite lengths before using the formula a/sin A = b/sin B.
2. You are given two lengths and a non-included angle and wish to find another angle. We link the two known lengths to their respective opposite angles and then use the same formula above.
1. You are given two angles and a length, and you wish to find the value of a second length. With the two angles, you can easily work out the third angle. We link the known length with its opposite length and the unknown length to calculate with its opposite lengths before using the formula a/sin A = b/sin B.
2. You are given two lengths and a non-included angle and wish to find another angle. We link the two known lengths to their respective opposite angles and then use the same formula above.
In part b, we have the two lengths and the sandwiched (included) angle, so we apply the cosine rule to solve the problem.
In part c, I link the known length to its opposite angle, the unknown length to its opposite angle and then use the sine rule accordingly.
In part c, I link the known length to its opposite angle, the unknown length to its opposite angle and then use the sine rule accordingly.
for the sine rule what does the non included length mean
Sorry, it’s “included ANGLE”
thx :)
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