Calculating length of AD

Question

I have the following question:

for question I have worked out question a) and b) i) to be 17.4,

however i'm not sure how to do question b)ii) as I know that AD is not half of AC is there a formula I should use to find this ?

Answer 1

For part a) use $$9^2=5^2+7^2-2\cdot5\cdot 7\cos(\beta)$$ For part b)$$S=\frac{5\cdot 7}{2}\sin(\beta)$$ For part c)$$\sin(\alpha)=\frac{BD}{5}$$($$\alpha$$ must be calculated.)

Answer 2

1. step: By cosine rule calculate $\angle ABC$

2. step: By Heron formula calulate the area of triangle

3. step: Calulate $BD$ with formula $$Area = {BD\cdot AC \over 2}$$

4. step: Use a Pyhtagora theorem in triangle $ABD$.

Answer 3

You have answered b)i) so you know the area of rectangle $A$, right? You can evaluate $BD$ from the following expression:

$$A =\frac{1}{2}AC\cdot BD$$

After that, you can calculate $AD$ from Pithagora's:

$$ AD^2+BD^2=AB^2$$