Question

Pg 23, q36 How do I figure this out? thanks

Answer 1

`AC~~5.12`
`BD~~9.67`

Explanation:

We the following things:

• `AB=DC=3.7`
• `CB=AD=6.8`
• `/_ABC=/_ADC=48`

We can use the cosine rule to find out `AC` and `BD`

`c^2=a^2+b^2-2bcosC`

`C=48`
`a=6.8`
`b=3.7`

`AC=c=sqrt(6.8^2+3.7^2-2(6.8*3.7)cos48)~~5.12`

Co-interior angles add up to `180^circ`.

So, `/_BAD=/_BCD=180-48=132`

Again, we can use the cosine rule, but replace `48` with `132`

`C=132`
`a=6.8`
`b=3.7`

`BD=c=sqrt(6.8^2+3.7^2-2(6.8*3.7)cos132)~~9.67`

`AC~~5.12`
`BD~~9.67`