Question

if a triangle has a hypotenuse with a length of 12 cm and a leg with a length of 10 cm, how long is the other leg rounded to the nearest tenth?

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse \(c = 12\) cm and one leg \(a=10\) cm. The Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), so \(b^{2}=c^{2}-a^{2}\).
Substitute the values: \(b^{2}=12^{2}-10^{2}\).

Step2: Calculate \(b^{2}\)

\(b^{2}=144 - 100=44\).

Step3: Find \(b\)

\(b=\sqrt{44}\approx6.6\) (rounded to the nearest tenth).

Answer:

\(6.6\) cm