ATAR Notes: Forum

HSC Stuff => HSC Maths Stuff => HSC Subjects + Help => HSC Mathematics Advanced => Topic started by: Piccolo on March 04, 2017, 06:37:11 pm

Title: Cosine Rule Help
Post by: Piccolo on March 04, 2017, 06:37:11 pm: Hey there!

Just struggling a bit with this question, mainly part ii). Thanks!
Title: Re: Cosine Rule Help
Post by: jamonwindeyer on March 04, 2017, 06:46:16 pm: Quote from: Piccolo on March 04, 2017, 06:37:11 pm
Hey there!

Just struggling a bit with this question, mainly part ii). Thanks!

Hey Piccolo! Welcome to the forums! ;D

This question just relies on writing out the cosine rule for the triangle - From there, it is algebraic stuff! So if you've got Part A, Part B won't be too much harder ;)

$a^2=b^2+c^2-2bc\cos{A}\implies43^2=48^2+x^2-2(48)(x)\cos{60}$

This simplifies down to a quadratic that you can factorise and solve (or use the quadratic formula if you prefer, but that is a little messier) to find your two values of $x$ ;D

$1849=2304+x^2-48x\\x^2-48x+455=0\\(x-13)(x-35)=0\\x=13, 35$

Does that make sense? :)