Mathematics: Can i have some ? i don t know how to do question e.

I think the answer would be Ehope this helps...

Can i have some ? i don t know how to do question

rose200215

30.12.2021

see explanation

Step-by-step explanation:

Using the exact trigonometric values

cos30° = $\frac{\sqrt{3} }{2}$ , sin30° = $\frac{1}{2}$ and tan45° = 1

Let the point where the segment from C meets AB be D, then

Using ΔBCD

cos30° = $\frac{adjacent}{hypotenuse}$ = $\frac{BD}{x}$ and

$\frac{BD}{x}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2BD = $\sqrt{3}$ x ( divide both sides by 2 )

BD = $\frac{\sqrt{3} }{2}$ x ←

sin30° = $\frac{opposite}{hypotenuse}$ = $\frac{CD}{x}$ and

$\frac{CD}{x}$ = $\frac{1}{2}$ ( cross- multiply )

2CD = x ( divide both sides by 2 )

CD = $\frac{1}{2}$ x

Using ΔACD

tan45° = $\frac{opposite}{adjacent}$ = $\frac{CD}{AD}$ = $\frac{\frac{x}{2} }{AD}$ = 1 , hence

AD = $\frac{1}{2}$ x ←

Hence

AB = BD + AD = $\frac{\sqrt{3} }{2}$ x + $\frac{1}{2}$ x = ( $\frac{\sqrt{3}+1 }{2}$ ) x

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