Question

problem 2 calculate the exact value of the unknown side length in the triangle. 2 5 ?

Explanation:

Step1: Identify the triangle type

The triangle is a right - triangle (as there is a right - angle symbol). Let the hypotenuse be \(c = 5\), one leg be \(a = 2\), and the unknown leg be \(b\). We use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\).

Step2: Rearrange the formula to solve for \(b\)

From \(a^{2}+b^{2}=c^{2}\), we can get \(b^{2}=c^{2}-a^{2}\). Substitute \(a = 2\) and \(c = 5\) into the formula: \(b^{2}=5^{2}-2^{2}\).

Step3: Calculate the values

First, calculate \(5^{2}=25\) and \(2^{2}=4\). Then \(b^{2}=25 - 4=21\).

Step4: Find the value of \(b\)

Take the square root of both sides. Since \(b\) represents the length of a side, \(b=\sqrt{21}\) (we take the positive square root because length cannot be negative).

Answer:

\(\sqrt{21}\)