## AonZ 3 years ago 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.

1. AonZ

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2. AonZ

@jim_thompson5910 @Mertsj help pls

3. AonZ

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

4. Loser66

5. AonZ

im sorry ADB is theta :P

6. Loser66

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

7. Mertsj

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8. AonZ

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

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

10. Mertsj

Solve for cos theta

11. AonZ

ok yea i proved that part

12. AonZ

13. AonZ

how can we prove part b though?

14. Mertsj

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

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

16. AonZ

ok i solved it thank you