Question

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

Answer 1

Hi there!

R is equal to the value of

`4 √(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!

Answer 2

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=√(16\cdot2)\\r=√(16)\cdot\sqrt2\\r=4\sqrt2`


3.
Use trigonometric function:


`\sin45^o=(4)/(r)\\\\\sin45^o=(\sqrt2)/(2)\to(4)/(r)=(\sqrt2)/(2)\ \ \ |cross\ multiply\\\\r\sqrt2=8\ \ \ |\cdot\sqrt2\\\\2r=8\sqrt2\ \ \ |:2\\\\r=4\sqrt2`