Question

what is the length of side ac?
a
4.8
b
5.2
c
8.2
7.1
4.8
2.5

Explanation:

Step1: Identify triangle type

The triangle is right - angled at B, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with legs of length \(a\) and \(b\) and hypotenuse of length \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 4.8\) and \(b = 5.2\), and \(AC\) is the hypotenuse.

Step2: Apply Pythagorean theorem

First, calculate \(a^{2}\) and \(b^{2}\). \(a^{2}=(4.8)^{2}=4.8\times4.8 = 23.04\), \(b^{2}=(5.2)^{2}=5.2\times5.2 = 27.04\). Then, \(c^{2}=a^{2}+b^{2}=23.04 + 27.04=50.08\). Now, find \(c=\sqrt{50.08}\approx7.1\) (rounded to one decimal place).

Answer:

7.1