Answer:
[tex]e=\sqrt{f^{2}+d^{2}}[/tex]
Step-by-step explanation:
We are given that,
The acute angle of the right angled triangle is 65°.
Length of the side opposite to the acute angle = f
Length of the side adjacent to the acute angle = d
Length of the hypotenuse = e
Using 'Pythagoras Theorem', which states that 'the sum of square of length of the sides of a right triangle is equal to the square of the length of the hypotenuse'.
i.e. [tex]Hypotenuse^{2}=Opposite^{2}+Adjacent^{2}[/tex]
i.e. [tex]e^{2}=f^{2}+d^{2}[/tex]
i.e. [tex]e=\pm \sqrt{f^{2}+d^{2}}[/tex]
As, the length of the hypotenuse cannot be negative.
So, the expression showing the value of e is [tex]e=\sqrt{f^{2}+d^{2}}[/tex].