What is the value of x in the diagram below

Asked by maham237 @ 16/07/2021 in Mathematics viewed by 288 People

Answered by maham237 @ 16/07/2021

Hi,
The answer will be $\frac{ 18\sqrt{2} }{ \sqrt{3} }$ .

Now how is that, there is a rule for the right angled triangle which says:

cosθ = $\frac{adjacent side}{hypotenuse}$ so, if we applied this rule on the lower triangle we can say: cos30°= $\frac{9}{hypotenuse}$ and therefore the hypotenuse = $\frac{9}{cos30}$ = $\frac{18}{ \sqrt{3} }$ .

now in the upper triangle we will apply the same rule so,
cos45°= $\frac{adjacent side}{hypotenuse}$
and the adjacent side in the upper triangle is $\frac{18}{ \sqrt{3} }$ and the hypotenuse is x.
so cos45°= $\frac{( \frac{18}{ \sqrt{3} } )}{x}$ and then we can say
x= $\frac{ \frac{18}{ \sqrt{3} } }{cos45}$ = $\frac{ 18\sqrt{2} }{ \sqrt{3} }$ .

What is the value of x in the diagram below

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