Question

Find the value of each variable x= y= z=

Answer 1

Answer:

Step-by-step explanation:

A 45 degree angle in a right triangle produces 2 equal sides. In this case z and the perpendicular line are equal. So that's were we'll start. Then you move on to the 60 degree angle to get x and y.

Finding z

z^2 + z^2 = (24√2)                    Combine the left

2z^2 = 24^2 * 2                         Divide both sides by 2

2z^2/2 = 24^2/2

z^2 = 24^2                                 Take the square root of both sides

√z^2 = √24^2

z = 24

Finding x and y

The perpendicular = 24. Because it is a 60 degree angle that's given, we can do this without a calculator.

Tan 60 = opposite over adjacent

sqrt(3) = Perpendicular / z                      Multiply both sides by z

z*sqrt(3) = perpendicular

The above calculation tells us the perpendicular is 24

z*sqrt(3) = 24                                           Divide by sqrt 3

z = 24/√3

z = 24/1.73

z = 8√3

Finding x

Use Pythagoras to determine x

Perpendicular^2 + (8√3)^2 = x^2

24^2 + 8^2*3 = x^2

576 + 192 = x^2

768 = x^2

√x^2 = √768

x = 27.71