Question

Question 2

In the diagram, BCD is a straight line. AD = 2V3 cm
Work out the exact length of CD. Give your answer in the form
a + bv3 where a and b are integers
Not drawn
accurately
2V3 cm​

Answer 1

`CD=(3-√(3))\ cm`

Explanation:

step 1

Find the length side AB

In the right triangle ABD

`sin(30\°)=(AB)/(AD)`

`AB=sin(30\°)(AD)`

we have

`AD=2√(3)\ cm`

`sin(30\°)=(1)/(2)`

substitute

`AB=(1)/(2)(2√(3))`

`AB=√(3)\ cm`

step 2

Find the length side BD

In the right triangle ABD

`cos(30\°)=(BD)/(AD)`

`BD=cos(30\°)(AD)`

we have

`AD=2√(3)\ cm`

`cos(30\°)=(√(3))/(2)`

substitute

`BD=(√(3))/(2)(2√(3))`

`BD=3\ cm`

step 3

Find the length side BC

In the right triangle ABC

we know that

BC=AB -----> is an 45°-90°-45° triangle

therefore

`BC=√(3)\ cm`

step 4

Find the length side CD

we know that

`BD=BC+CD\\CD=BD-BC`

substitute the values

`CD=(3-√(3))\ cm`