James Ruse trig question (2 Viewers)

[droungk]

I am trawling through some old exams and this ruse question has taken advantage of me, i want my dignity back so can someone please help ?

A triangle ABC has angle C obtuse and and angle A twice that of angle B, all sides are integers.

Using the sine rule and the sin2@ and sin3@ formulae show that

a^2=b(b+c)

ps i dont know how to use computers they piss me of so much so i hope this works <= (what the hell is that?)

 

[nike33]

b/sin@ = a/2sin@cos@ = c/(3sin@-4sin^3@)
b = a/2cos@ = c/(4cos^2@-1)
a/b = 2cos@

b = c / ((a^2/b^2) - 1)
giving a^2 = b(b+c)

i wish we got qns like that in our papers

 

[+Po1ntDeXt3r+]

ruse questions arent actualli beyond the syllabus.. cept for some Q8 and mofo questions in the yr 11 paper..

its the time management that will kill ppl.. and speed
the questions in ruse papers are usually straight forward..

just draw a diagram..

then write out sine rule.. sin 2@ n
then fill in the sine rule..

then use the sine 2@= 2sin@cos@
and sin 3@=3sin@-4sin^3@

it should be
b/sin@ = a/2sin@cos@ = c/(3sin(pi-@)-4sin^3(pi-@))

cos the pi-3@ is the angle size of C and the teachers in ruse usualli need the explanation that sin @ = sin(pi-@) since sine is cyclic every pi .. otherwise nike33 is right..