High School

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Determine the values of x, y, and z

A

x=40.5, y 16.8, and z = 12.6

B

x=43.2, y 19.9, and z = 23.9

C x 41.7, y = 20.2, and z = 21.8

D

x=38.8, y = 13.9, and z = 12.8

Z

x

30

36

Determine the values of x y and z A x 40 5 y 16 8 and z 12 6 B x 43 2 y 19

Answer :

The value of x = 43.2, y = 19.9, and z = 23.9.

How to calculate the value of x, y and z?

The value of x, y and z is calculated by applying the following formula as shown below.

Using Pythagoras theorem, the value of y is;

y² = 36² - 30²

y² = 396

y = √396

y = 19.9

The value of z is calculated as follows;

z² = x² - 36² ------ (1)

z² = y² + (x - 30)² ------ (2)

from equation (2), we will have;

z² = y² + x² - 60x + 900

z² = 396 + x² - 60x + 900

Solve simplified equation (2) and (1) simultaneously,

x² - 36² = 396 + x² - 60x + 900

60x = 396 + 36² + 900

60x = 2,592

x = 2,592 / 60

x = 43.2

The value of z is calculated as follows;

z² = 43.2² - 36²

z² = 570.24

z = √570.24

z = 23.9

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