Question

What is the value of r? Please answer in exact value

Answer 1

We have three different ways to the solution.

1.
It's a right triangle and isosceles triangle.
The formula of the hypotenuse of this triangle:
h - the hypotenuse
a - the leg

$h=a\sqrt2$

therefore

$r=4\sqrt2$


2.
Use the Pythagorean theorem:

$r^2=4^2+4^2\\r^2=16+16\\r^2=16\cdot2\\r=\sqrt{16\cdot2}\\r=\sqrt{16}\cdot\sqrt2\\r=4\sqrt2$


3.
Use trigonometric function:

$\sin45^o=\dfrac{4}{r}\\\\\sin45^o=\dfrac{\sqrt2}{2}\to\dfrac{4}{r}=\dfrac{\sqrt2}{2}\ \ \ |cross\ multiply\\\\r\sqrt2=8\ \ \ |\cdot\sqrt2\\\\2r=8\sqrt2\ \ \ |:2\\\\r=4\sqrt2$

Answer 2

Hi there!

R is equal to the value of
$4 \sqrt{2}$
Or 5.7 in decimal form

This is because of the 45-45-90 relationship.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!