The following figure shows triangle XY Z. The length of XY is 19 units, and the length of Y Z is 281 units.
What is the value of XZ\YZ?
To find the value of XZ/YZ, we first need to find the length of XZ.
Let's denote the length of XZ as "x".
By applying the Pythagorean theorem in triangle XYZ, we have:
XY^2 + XZ^2 = YZ^2
19^2 + x^2 = 281^2
361 + x^2 = 78961
x^2 = 78961 - 361
x^2 = 78600
x = sqrt(78600)
x ≈ 280.32
So, the value of XZ is approximately 280.32 units.
Now, we can find the value of XZ/YZ by dividing the length of XZ by the length of YZ:
XZ/YZ = 280.32/281
XZ/YZ ≈ 0.996
Therefore, the value of XZ/YZ is approximately 0.996.
how do you know it is a right triangle?
And usually side XZ would be denoted y, since it is opposite angle Y
We do not have enough information to determine if it is a right triangle based on the information provided in the question. I apologize for the incorrect assumption in my previous response.
Given that side XY is 19 units, and side YZ is 281 units, we can still find the length of side XZ using the triangle inequality theorem:
XZ < XY + YZ
XZ < 19 + 281
XZ < 300
Now let's denote the length of XZ as "y".
By applying the triangle inequality to the given values, we know that the length of side XZ (y) must be less than 300 units.
Now we have the equation to solve for y in terms of XY and YZ:
y > YZ - XY
y > 281 - 19
y > 262
Therefore, the value of XZ (y) is greater than 262 units.
Given that XZ > 262 and YZ = 281, we can find the ratio of XZ to YZ:
XZ/YZ > 262/281
XZ/YZ > 0.932
Therefore, the value of XZ/YZ is greater than 0.932.