Question

Find the values of x and y​

Answer 1

Hello from MrBillDoesMath!

Answer:

x = 5 * sqrt(2)

5 = y

Discussion:

First thing: the hypotenuse is the side opposite the right (90 degree) angle. So it is side x NOT side y as shown in your diagram.  

The triangle is a 45-45-90 triangle so

tan(45) = y/5            => as tan(45) = 1

1 = y/5                      => multiply both sides by 5

5 = y

If you don't care for the trig approach, since it's a 45-45-90 triangle the length of the legs are that same, i.e y = 5

Also sin(45) = y/x    => as y = 5

sin(45) = 5/x            => as sin(45) = sqrt(2)/2

sqrt(2)/2 = 5/x         => multiply bot sides by x

x* sqrt(2)/2 = 5/x * x = 5   =>

x* sqrt(2)/2 = 5         => divide both sides by sqrt(2)/2

x = 5 * (2/sqrt(2))

x = 5 * sqrt(2)

Or if you don't care for the trig approach, simply apply the Pythagorean theorem ( 5^2 + 5^2 = x^2) and solve for x

Thank you,

MrB