The exact value of x in the right triangle is determined as 4√3.
How to calculate the exact value of x?
The exact value of x is calculated by applying the following formula as shown below;
The given side lengths of the triangle;
hypothenuse side = 8
adjacent leg = x
Let the opposite leg = y
Using Pythagoras theorem, the value of x is calculated as;
x² = 8² - y² ----- (1)
Considering the smaller right triangle with base length of 2, we will have the following equation;
h² = y² - 2² ------ (2)
Considering the second part of the triangle;
h² = x² - (8 - 2)²
h² = x² - 6² ---- (3)
Substitute (3) into (2)
x² - 6² = y² - 2²
y² = x² - 6² + 2²
y² = x² - 32 ----- (4)
Substitute (4) into (1)
x² = 8² - y²
x² = 8² - (x² - 32)
x² = 64 - x² + 32
2x² = 96
x² = 96/2
x² = 48
x = √48
x = 4√3