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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​

Question 2In the diagram BCD is a straight line AD 2V3 cmWork out the exact length of CD Give your answer in the forma bv3 where a and b are integersNot drawnac class=

Respuesta :

calculista

Answer:

[tex]CD=(3-\sqrt{3})\ cm[/tex]

Step-by-step explanation:

step 1

Find the length side AB

In the right triangle ABD

[tex]sin(30\°)=\frac{AB}{AD}[/tex]

[tex]AB=sin(30\°)(AD)[/tex]

we have

[tex]AD=2\sqrt{3}\ cm[/tex]

[tex]sin(30\°)=\frac{1}{2}[/tex]

substitute

[tex]AB=\frac{1}{2}(2\sqrt{3})[/tex]

[tex]AB=\sqrt{3}\ cm[/tex]

step 2

Find the length side BD

In the right triangle ABD

[tex]cos(30\°)=\frac{BD}{AD}[/tex]

[tex]BD=cos(30\°)(AD)[/tex]

we have

[tex]AD=2\sqrt{3}\ cm[/tex]

[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]

substitute

[tex]BD=\frac{\sqrt{3}}{2}(2\sqrt{3})[/tex]

[tex]BD=3\ cm[/tex]

step 3

Find the length side BC

In the right triangle ABC

we know that

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

therefore

[tex]BC=\sqrt{3}\ cm[/tex]

step 4

Find the length side CD

we know that

[tex]BD=BC+CD\\CD=BD-BC[/tex]

substitute the values

[tex]CD=(3-\sqrt{3})\ cm[/tex]

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