Home
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
__________________________________________________________________________
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.
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.
