Question

Geometry thats finding x y and z of a triangle but my dum self doesn't know this so plz help

Answer 1

`x = (48)/(√(3))`

`y = (24)/(√(3) )`

`z = 24`

Explanation:

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FACTS TO KNOW BEFORE SOLVING :-

For a triangle with one of it's acute angle α (alpha) , the value of :-

• 
  `\sin \alpha = (Side \: opposite \: to \: \alpha )/(Hypotenuse)`

• 
  `\cos \alpha = (Side \: adjacent \: to \: \alpha)/(Hypotenuse)`

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In the question , first of all lets find the value of z. So,

`\cos 45 = (z)/(24√(2))`

`=> (1)/(√(2)) = (z)/(24√(2))`

`=> z = (24√(2))/(√(2)) = 24`

Length of the altitude perpendicular to side (z + y) =
`\sqrt{(24√(2))^2 - 24^2} = 24`

Now , lets find the value x. So,

`\sin 60 = (24)/(x)`

`=> (√(3))/(2) = (24)/(x)`

`=> x = (48)/(√(3))`

Also ,

`\cos 60 = (y)/(x)`

`=> (1)/(2) =(y)/((48)/(√(3)))`

`=> y = (48)/(2√(3)) = (24)/(√(3))`