Question

find the length of the third side. if necessary, round to the nearest tenth. 20 15

Explanation:

Step1: Identify triangle type (right triangle)

This is a right - triangle, so we use the Pythagorean theorem, which states that for a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(c^{2}=a^{2}+b^{2}\) (or if we want to find a leg, \(a^{2}=c^{2}-b^{2}\), but in this case, the two given sides are the legs, and we need to find the hypotenuse). Let \(a = 15\) and \(b=20\).

Step2: Apply the Pythagorean theorem

We calculate \(c^{2}=15^{2}+20^{2}\). First, find \(15^{2}=225\) and \(20^{2}=400\). Then \(c^{2}=225 + 400=625\).

Step3: Find the length of \(c\)

Take the square root of \(c^{2}\) to find \(c\). Since \(c=\sqrt{625}\), and \(\sqrt{625} = 25\).

Answer:

25