Hi there all..

Someone asked me on facebook for help with ambigous cases in 2.5

So i think ill post my response here to in case anyone else *COUGH ROGER WU**COUGH maybe KEVIN* is having trouble with it

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I dont know if this makes sense, but if its an is an ambiguos case, line AC can touch line BC at 2 different points. But dont worry about that for now.

... See more

B=28°

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A C

So what you do is.

Check : Exercise 2.5 Question 2f)

1. b÷sinB = a÷sinA

2. 28÷sin28 = 56÷sinA

3. (56 x sin28)÷ 28 = sinA

and that gives

Angle A = 69°52'

Now im sure you already know how to do all that

So if this case is an ambiguous case there can be 2 values for angle A - One value is 69°52 (acute value)'... and the other has to be

180° - 69°52'

180 - 69°52' = 110° 08'' (obtuse value)

Angle A can be either 69°52' or 110° 08'

But the you have to check if it is an ambiguos case or not..

To do that we have to add up the two angles we already know...

B + A

First Case = 28° + 69°52' (acute value) = Less than 180°

2nd Case (if ambiguous) = 28° + 110° 08' (obtuse value) = Less than 180°

Since they both add to LESS than 180° .. the case is an ambiguos one and you can write down that A = 69°52' or 110° 08' ...(obviously if they = more than 180° , there is no room left for the remaining angle (C) and it cant be a triangle.

Someone asked me on facebook for help with ambigous cases in 2.5

So i think ill post my response here to in case anyone else *COUGH ROGER WU**COUGH maybe KEVIN* is having trouble with it

__________________________________________________________________________

I dont know if this makes sense, but if its an is an ambiguos case, line AC can touch line BC at 2 different points. But dont worry about that for now.

... See more

B=28°

/\

/ \

/_ __\

A C

So what you do is.

Check : Exercise 2.5 Question 2f)

1. b÷sinB = a÷sinA

2. 28÷sin28 = 56÷sinA

3. (56 x sin28)÷ 28 = sinA

and that gives

Angle A = 69°52'

Now im sure you already know how to do all that

So if this case is an ambiguous case there can be 2 values for angle A - One value is 69°52 (acute value)'... and the other has to be

180° - 69°52'

180 - 69°52' = 110° 08'' (obtuse value)

Angle A can be either 69°52' or 110° 08'

But the you have to check if it is an ambiguos case or not..

To do that we have to add up the two angles we already know...

B + A

First Case = 28° + 69°52' (acute value) = Less than 180°

2nd Case (if ambiguous) = 28° + 110° 08' (obtuse value) = Less than 180°

Since they both add to LESS than 180° .. the case is an ambiguos one and you can write down that A = 69°52' or 110° 08' ...(obviously if they = more than 180° , there is no room left for the remaining angle (C) and it cant be a triangle.