Oh gawd, trig with obtuse angles, :@ (1 Viewer)

[Anthrax]

i havent done a question on this in ages. it looks well complicated.

any tips ?

 

[Digital_Spork]

a/sinA = b/sinB = c/sinC
or the other way round...

c^2 = a^2+b^2 - 2*ab Cos C
Square root the answer then
= the lenth of the unknown side...

CosA = c^2+b^2 - a^2/2bc
then hit = .. then use the bubble button...(the degrees)

I cant think of much else really apart from all angles in triangle add up to 180 degrees

 

[Michala]

with obtuse angles i think all u need to remember that....

in the first 90' of all (cos, sin and tan) are positive, in the next sector 90-180, ONLY sin is positive (the others are negative) 180-270 tan is positive (cos and sin are negative) and 270-360 cos is positive (tan and sin negative).

so therefore... for an obstuse angle (90-180)

Sin (180 - angle size) = Sin+
Cos (180- angle) = Cos -
Tan (180-angle) = Tan -


i agree its kinda weird and complicated... try practicing a few questions


good luck

 

[Dr_Doom]

Oooo I remember all that. The "ALL STATIONS TO CENTRAL" thing.

ALL (0 - 90) - All are positive
STATIONS (90 - 180) - Sin is positive
TO (180 - 270) - Tan is positive
CENTRAL (270 - 360) - Cos is positive

 

[PC]

For the general course, it's no stress. There are basically three (or four) rules:

Sine Rule
a/sin A = b/sin B

Cosine Rule (for a side)
a² = b² + c² – 2bc cos A

Cosine Rule (for an angle)
cos A = (b² + c² – a²)/(2bc)

Area Rule
Area = 1/2 x ab sin C

BUT ... many people will probably disagree with me, especially days before the HSC, but I think it's easier to remember these rules in words, so you don't have to get stressed on thinking what is a, b and c and all that.

1. The sine rule needs two sides and the two OPPOSITE angles. One of these will be what you're trying to find. If you can't find that in your diagram then you can't use the sine rule. You'll probably need the cosine rule. To use the sine rule, remember:
side over SINE of the opposite angle equals side over SINE of the opposite angle

2. To find a side using the cosine rule you will need the other two sides and the angle in between them. That's it. Two sides and the angle in between them, then the rule is:
unknown side squared = first side squared + second side squared - two times the first times the second times COS of the angle in between them.
Do it all in one go on the calculator. Don't forget to take the square root at the end, just like pythagoras' theorem.

3. To find an angle using the cosine rule you will need all three sides ... but look at the side which is opposite the angle you're trying to find cause we treat that one differently. The rule is:
COS of the angle = (first side squared + second side squared – opposite side squared) over (two times first side times second side)
The side opposite the angle you're trying to find is only used in the top line of the fraction.
Remember to use brackets when you put this into the calculator, otherwise you come unstuck with order of operations.
AND don't forget, this gives you the cosine of the angle NOT the angle, so you'll have to press [Shift][cos] or something like that to find the actual angle.

4. For the area of any triangle you'll need any two sides and the angle in between them. This one's easy. The rule is:
Area = 1/2 times first side times second side times SINE of the angle in between them
And there's the area!

It works for me. Someone else might find this useful maybe.

All the best everyone.