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Pls help me with this C3 trig question!!!

22) Given that tanA=1/5 and tanB=2/3, find the value of A+B,
a) Where A and B are both acute.
b) Where A is reflex and B is acute.

I tried to do part a) and used the triangle method to find the third side using pythagoras' theorem. For tanA i got √26 and for tanB i got √13, but then they're both in the 1st quadrant, so tanA=1/5 and tanB=2/3? Then I got something terribly wrong!!! :confused:

:confused:

OP

Oh and another question asks: Two of the angles, A and B, in triangle ABC are such that tanA=3/4 and tanB=5/12.
a) find the exact value of i) sin(A+B) ii) tan2B.
It doesnt say if the angles are acute, reflex...etc etc. How am i supposed to know which quadrant they're in?

EDIT: I've just done it and got it right...I just assumed they were both acute. :confused:

:confused:

turtle2

22) Given that tanA=1/5 and tanB=2/3, find the value of A+B,
a) Where A and B are both acute.
:

Here is first part

Picture 10.png20.0KB

Use steves methods, if thats what is required for full marks but it would be alot faster to do.

actan1/5+arctan2/3=45°
arctan = tan inverse

OP

thanks! What about the second part?

turtle2

22) Given that tanA=1/5 and tanB=2/3, find the value of A+B,
b) Where A is reflex and B is acute.
:

Second solution.

Picture 14.png22.1KB

turtle2

Oh and another question asks: Two of the angles, A and B, in triangle ABC are such that tanA=3/4 and tanB=5/12.
a) find the exact value of i) sin(A+B) :

Here is my solution ... you had better check it for errors

Picture 15.png31.6KB

turtle2

Oh and another question asks: Two of the angles, A and B, in triangle ABC are such that tanA=3/4 and tanB=5/12.
ii) tan2B. :

Here is the value of tan2B

Picture 17.png21.8KB

OP

steve2005

Here is my solution ... you had better check it for errors

I got 56/65 and that's the answer in the book as well.

turtle2

I got 56/65 and that's the answer in the book as well.

Yes, I made a mistake. I wrote 3 instead of 5

Here is corrected version.

Picture 19.png53.0KB

OP

And then part b) says: by writing C as 180-(A+B), show that cosC=-33/65

turtle2

And then part b) says: by writing C as 180-(A+B), show that cosC=-33/65

Here is my solution. Don't forget to check for errors.

Picture 20.png40.4KB

OP

Thanks a loooot!

Could i ask 2/3 more Qs? They're from the C3 book? Should i post the questions or just the ex. number and Q number?

turtle2

Thanks a loooot!

Could i ask 2/3 more Qs? They're from the C3 book? Should i post the questions or just the ex. number and Q number?

post number

OP

ex. 7F, Qs 1, 3 and 4.

turtle2

ex. 7F, Qs 1, 3 and 4.

First part
You draw a sketch and try and finish Q1

Picture 21.png18.2KB

OP

steve2005

First part
You draw a sketch and try and finish Q1

Oh, i could do the first part! I just didnt know how to work out the angle.

turtle2

Oh, i could do the first part! I just didnt know how to work out the angle.

Here is a diagram.

Picture 22.png9.1KB

OP

Ok, thanks!!

turtle2

Ok, thanks!!

Question 3 and 4 Ex 7F

Picture 24.png58.3KB

Picture 25.png34.8KB

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