## AonZ Group Title Yr11 3unit question help pls! ABC is a triangle and D is the midpoint of AC. BD=m and angle ADB = theta (a) show that cos(theta) = 4m^2 + b^2 - 4c^2 / 4mb and write an expression for cos(180-theta). (b) show a^2 +c^2 = 2m^2 + 1/2 b^2 I have done part (a) and need help on part (b) pls. one year ago one year ago

1. AonZ Group Title

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2. AonZ Group Title

@jim_thompson5910 @Mertsj help pls

3. AonZ Group Title

umm im pretty sure ADC is 180. Why wouldnt it be?

4. Loser66 Group Title

5. AonZ Group Title

im sorry ADB is theta :P

6. Loser66 Group Title

ok, let tag someone who is good at geometry and trig @Mertsj

7. Mertsj Group Title

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8. AonZ Group Title

hmm yes i proved part a but i couldnt get part b. I think you need to do something with part a to get part b

9. Mertsj Group Title

$c^2=m^2+(\frac{b}{2})^2-2m(\frac{b}{2})\cos \theta$

10. Mertsj Group Title

Solve for cos theta

11. AonZ Group Title

ok yea i proved that part

12. AonZ Group Title

13. AonZ Group Title

how can we prove part b though?

14. Mertsj Group Title

From the first part you have an expression for cos (180-theta) Get another expression for cos (180-theta) using triangle BCD Equate those two expressions for cos(180-theta) and solve for a^2+b^2

15. AonZ Group Title

- 4m^2 + b^2 - 4c^2 / 4mb = 4m^2 + b^2 - 4a^2 / 4mb right?

16. AonZ Group Title

ok i solved it thank you