Given:
Base of a right triangle = 7 in
Height of a right triangle = a
Hypotenuse = 16 in
To find:
The length of side a.
Solution:
Using Pythagoras theorem:
[tex]\text{Base}^2+\text{Height}^2=\text{Hypotenuse}^2[/tex]
[tex]7^{2}+a^{2}=16^{2}[/tex]
[tex]49+a^{2}=256[/tex]
Subtract 49 from both sides.
[tex]49+a^{2}-49=256-49[/tex]
[tex]a^{2}=207[/tex]
Taking square root on both sides, we get
a = 14.4
The length of side a is 14.4 in.