Question

Find the value of z and simplify completely.

Answer 1

Answer:

z = 6√2 = 8.49

Step-by-step explanation:

In this question, we are to find the value of the length z.

Mathematically, using Pythagoras’s theorem we can do this.

The Pythagoras’ theorem states that the square of the length of the hypotenuse equals the sum of the length of the squares of the two other sides.

Kindly note that the hypotenuse is the side that faces the angle 90

These are the points needed to solve for z

Using Pythagoras,

z^2 = y^2 + 4^2

z^2 = y^2 + 16 •••••••(i)

x^2 + z^2 = 20^2

x^2 + z^2 = 400 •••••••••(ii)

z^2 + 16^2 = x^2. ••••••••(iii)

Substitute iii into ii

z^2 + 16^2 + z^2 = 400

2z^2 + 256 = 400

2z^2 = 400-256

2z^2 = 144

z^2 = 72

z = √(72)

z = 6√2