More Trig Help *Thanks Guys* :) (1 Viewer)

[x___y]

Help with Part B of question 19, and question 20 please

 

[slightly_above_average]

19 b
qr/sinb=a/2sin90 (sin rule)

qr=sinb*a*1/2

yea also b is 45 degrees cause like triangles and it bisects
cos(45)^2=1/2
cos(b)^2=1/2

qr=sinb*a*cos(b)^2


20 im not bothered but like if you apply the symmetry on the two triangles and minus like big from small you should get it i think.

 

[CM_Tutor]

19 b
qr/sinb=a/2sin90 (sin rule)

qr=sinb*a*1/2

yea also b is 45 degrees cause like triangles and it bisects
cos(45)^2=1/2
cos(b)^2=1/2

qr=sinb*a*cos(b)^2


20 im not bothered but like if you apply the symmetry on the two triangles and minus like big from small you should get it i think.

Angle is not ... if it was would be , which does not appear true given the diagram.

Also, the use of the sine rule at the start appears to assume that is the midpoint of , which is not given in the question.

----

Let .

Then (angle sum of ).

Then (angle sum of line ).

Then (angle sum of ).

Then (angle sum of line ).

Then (angle sum of ).

Now, in .

And, in .

And, using the Pythagorean identity .

So, using , as required.

 

[gendu]

Angle is not ... if it was would be , which does not appear true given the diagram.

Also, the use of the sine rule at the start appears to assume that is the midpoint of , which is not given in the question.

----

Let .

Then (angle sum of ).

Then (angle sum of line ).

Then (angle sum of ).

Then (angle sum of line ).

Then (angle sum of ).

Now, in .

And, in .

And, using the Pythagorean identity .

So, using , as required.

...............………………………….¸„„„„ …………………….…………...„--~'¯…….'\ ………….…………………… („-~~--„¸_….,/ì'Ì …….…………………….¸„-^"¯ : : : : :¸-¯"¯/' ……………………¸„„-^"¯ : : : : : : : '¸„„,-" **¯¯¯'^^~-„„„----~^'"¯ : : : : : : : : : :¸-" .:.:.:.:.„-^" : : : : : : : : : : : : : : : : :„-" :.:.:.:.:.:.:.:.:.:.: : : : : : : : : : ¸„-^¯ .::.:.:.:.:.:.:.:. : : : : : : : ¸„„-^¯ :.' : : '\ : : : : : : : ;¸„„-~" :.:.:: :"-„""**/'ì¸'¯ :.': : : : :"-„ : : :"\ .:.:.: : : : :" : : : : , :.: : : : : : : : : : : : 'Ì : : : : : : :, : : : : : :/ "-„::::„-*__„„~"

 

[slightly_above_average]

...............………………………….¸„„„„ …………………….…………...„--~'¯…….'\ ………….…………………… („-~~--„¸_….,/ì'Ì …….…………………….¸„-^"¯ : : : : :¸-¯"¯/' ……………………¸„„-^"¯ : : : : : : : '¸„„,-" **¯¯¯'^^~-„„„----~^'"¯ : : : : : : : : : :¸-" .:.:.:.:.„-^" : : : : : : : : : : : : : : : : :„-" :.:.:.:.:.:.:.:.:.:.: : : : : : : : : : ¸„-^¯ .::.:.:.:.:.:.:.:. : : : : : : : ¸„„-^¯ :.' : : '\ : : : : : : : ;¸„„-~" :.:.:: :"-„""**/'ì¸'¯ :.': : : : :"-„ : : :"\ .:.:.: : : : :" : : : : , :.: : : : : : : : : : : : 'Ì : : : : : : :, : : : : : :/ "-„::::„-*__„„~"

theyre similar...

 

[CM_Tutor]

Earlier in this thread, I wrote that:

Angle

is not

... if it was

would be

, which does not appear true given the diagram.

I need to point out that my statement that "

would be

" if angle

is

is inaccurate, the result of a mistake on my part. Angle

being

does not mean that

must be

as a consequence. My apologies for the mistake.

I maintain, however, that I see nothing in the question that supports drawing the conclusion that angle

must be

, but it is one possible value for angle

. I do not think that an answer that was based on an unproven declaration that angle

must be

or that must bisect would gain much credit.

 

[CM_Tutor]

...............………………………….¸„„„„ …………………….…………...„--~'¯…….'\ ………….…………………… („-~~--„¸_….,/ì'Ì …….…………………….¸„-^"¯ : : : : :¸-¯"¯/' ……………………¸„„-^"¯ : : : : : : : '¸„„,-" **¯¯¯'^^~-„„„----~^'"¯ : : : : : : : : : :¸-" .:.:.:.:.„-^" : : : : : : : : : : : : : : : : :„-" :.:.:.:.:.:.:.:.:.:.: : : : : : : : : : ¸„-^¯ .::.:.:.:.:.:.:.:. : : : : : : : ¸„„-^¯ :.' : : '\ : : : : : : : ;¸„„-~" :.:.:: :"-„""**/'ì¸'¯ :.': : : : :"-„ : : :"\ .:.:.: : : : :" : : : : , :.: : : : : : : : : : : : 'Ì : : : : : : :, : : : : : :/ "-„::::„-*__„„~"

Gendu, looking at your attachment, I see pairs of similar triangles but no congruent triangles (though there would be congruent triangles if angle was required to be ).

As for the above string of characters, I have no idea what it is.

Finally... yes, I am a Mod, but that doesn't mean that I never make mistakes or am always right. I'm fine with people questioning me, pointing out mistakes, etc. I encourage everyone to look at each post on its merits. The fact that a post is made from someone who has a track record of useful / helpful / correct posts is a reason to reflect if something seems to be wrong, but not to accept a post as true just because of who posted it.