Question

The picture shows a triangular island: A right triangle is shown with an acute angle equal to 65 degrees. The length of the side of the triangle opposite to the acute angle is f. The length of the side of the triangle adjacent to the acute angle is d. The length of the hypotenuse is e. Which expression shows the value of e?

Answer 1

Answer:

$e=\sqrt{f^{2}+d^{2}}$

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. $Hypotenuse^{2}=Opposite^{2}+Adjacent^{2}$

i.e. $e^{2}=f^{2}+d^{2}$

i.e. $e=\pm \sqrt{f^{2}+d^{2}}$

As, the length of the hypotenuse cannot be negative.

So, the expression showing the value of e is $e=\sqrt{f^{2}+d^{2}}$.