find x in the diagram.Both the x are equal
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if we use Pythagorean triplet then it will 5²+x=13²
salehabaseer9:
what if we had to use trigonometrical ratios
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In 1st triangle with sides 13 , 5 and X+Y
By Pythagoras theorem ,
13² = 5² + (X+Y)²
169 - 25 = (X+Y)²
(X+Y)² = 144
X+Y = 12
X= 12-Y (1)
In 2nd triangle with sides 13 , Y and X+5
By Pythagoras theorem ,
13² = Y² + (X+5)²
169 = Y² + (12-Y+5)² [By (1)]
169 = Y² + (17-Y)²
169 = Y² + 289 -2*17*Y + Y²
2Y² - 34Y + 120=0
Y² - 17Y + 60=0
Y=12 or Y=5
If Y=12, By (1)
X=0
If Y=5, By (1)
X=7
By Pythagoras theorem ,
13² = 5² + (X+Y)²
169 - 25 = (X+Y)²
(X+Y)² = 144
X+Y = 12
X= 12-Y (1)
In 2nd triangle with sides 13 , Y and X+5
By Pythagoras theorem ,
13² = Y² + (X+5)²
169 = Y² + (12-Y+5)² [By (1)]
169 = Y² + (17-Y)²
169 = Y² + 289 -2*17*Y + Y²
2Y² - 34Y + 120=0
Y² - 17Y + 60=0
Y=12 or Y=5
If Y=12, By (1)
X=0
If Y=5, By (1)
X=7
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