maths prelim question (2 Viewers)

[girlworld_club]

How do you do all of question 5 c.

i am stuck and there are no solutions available.



thanks. don't mind the scribbling it's just some ideas i had, it is not the correct way of working out the answer.

 

[omgiloverice]

I am in the process of answering, but did you notice the mistake in the question?

 

[girlworld_club]

no i haven't.

 

[bedpotato]

no i haven't.

The question says that angle CED = theta, but the diagram says that angle CED = q.

 

[HeroicPandas]

For part (i) and (ii), draw out triangles CDE and ABC separately so that the right angle is really obvious - then find sin(theta)

(Hint: SOH CAH TOA)

(iii) Write out the result of (i) and (ii) and eliminate theta

(iv) cot(theta) = 1/tan(theta)

 

[girlworld_club]

where is the right angle for part ii?

 

[HeroicPandas]

where is the right angle for part ii?

Angle(ACB) as u've indicated in ur diagram

 

[bedpotato]

But you cannot assume that angle ACB is a right angle. That would be too easy for 3 marks. Since part ii) is 3 marks, you probably have to show that triangle ABC has a right angle and then use SOHCAHTOA to find sin(theta).

Edit: Lol. Even though you can't assume anything, I was wrong about having to prove there's a right angle in triangle ABC (spent half an hour trying to do this). As pdang said, the cos rule should be used.

 

[RealiseNothing]

I might be completely derping, but angle ACB can't be a right angle, it's impossible.

 

[RealiseNothing]

Yer, I'm not derping, angle ACB can't be 90.

 

[pdang]

cant you just use the cos rule since cos(90-q) = sin q

 

[HeroicPandas]

Yer, I'm not derping, angle ACB can't be 90.

I guided with the help of diagram and i used to brain power

BUt look

Angle(DCE) = 90-(theta) (angle sum of triangle is 180)
Angle(BAC) + angle(ACE) = 180 (co-interior angles)

 

[bedpotato]

Yer, I'm not derping, angle ACB can't be 90.

Why not? Sorry, I'm just confused as to why it can't be 90.

 

[HeroicPandas]

But you cannot assume that angle ACB is a right angle. That would be too easy for 3 marks. Since part ii) is 3 marks, you probably have to show that triangle ABC has a right angle and then use SOHCAHTOA to find sin(theta).

GOOD POINT!

i reckon girlworld lcub showed it was a right angle through angle geometry in her working out (UNLESS she just marked the stuff on the diagram and forgot to explain it in her working out...)

 

[RealiseNothing]

Why not? Sorry, I'm just confused as to why it can't be 90.

Assume ACB is 90, and since angle EDC Is 90, then . But this isn't possible as and so the two lines BC and DE shouldn't intersect. But they do intersect (at D), so our assumption must be wrong, that is ACB isn't 90.

 

[RealiseNothing]

Basically, if angle ACB is 90, it implies that which can't be true.

 

[HeroicPandas]

wowowowo

Angle(BAC) = theta?

how?

nah... thats a mistake lol (i was tricked...the millionth time...)

and @realisenothing - i like ur logic!

 

[pdang]

it isnt, the markings on the diagram are wrong.
i repeat cos rule anyone?

 

[RealiseNothing]

wowowowo

Angle(BAC) = theta?

how?

That's cos it's not.

 

[RealiseNothing]

it isnt, the markings on the diagram are wrong.
i repeat cos rule anyone?

Yep this.