Question

find the value of x.
right triangle with vertical leg 8, hypotenuse 12, horizontal leg x
x = ?
round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is hypotenuse, \(a,b\) are legs. Here, \(c = 12\), \(a = 8\), \(b = x\). So \(8^2 + x^2 = 12^2\).

Step2: Solve for \(x^2\)

\(x^2 = 12^2 - 8^2 = 144 - 64 = 80\).

Step3: Find \(x\)

\(x=\sqrt{80}\approx8.9\) (rounded to nearest tenth).

Answer:

\(8.9\)