Respuesta :
Answer:
- Given - a right triangle with length of one side = 5 units and with hypotenuse of length = 8 units.
By applying Pythagoras theorem ,
[tex]h {}^{2} = p {}^{2} + b {}^{2} \\ (8) {}^{2} = (5) {}^{2} + b {}^{2} \\ 64 = 25 + b {}^{2} \\ b {}^{2} = 64 - 25 \\ b {}^{2} = 39 \\ b = \sqrt{39 \:} \: units[/tex]
hope helpful~
We are given that , in a right angled triangle the hypotenuse is 8 units and it's one leg is 5 units . And we need to find the another leg . So , here Pythagoras theorem will be very helpful for us which states that in any Right Triangle , the sum of square of it's two sides ( base and perpendicular or two legs ) is equal to the square of it's largest side ( Hypotenuse )
Now , let's assume that the other leg be x , so now by Pythagoras theorem ;
[tex]{:\implies \quad \sf x^{2}+5^{2}=8^{2}}[/tex]
[tex]{:\implies \quad \sf x^{2}+25=64}[/tex]
[tex]{:\implies \quad \sf x^{2}=64-25}[/tex]
[tex]{:\implies \quad \sf x^{2}=39}[/tex]
Raising power to ½ on both sides will leave us with x = +√39 , -√39. But as length can never be -ve
[tex]{:\implies \quad \bf \therefore \underline{\underline{x=\sqrt{39}\:\: units}}}[/tex]
Hence , the another leg of the right angled triangle is √39 units
