Question

drag each length to the correct location on the triangle. each length can be used more than once, but not all lengths will bé used.
what are the missing side lengths for the triangle?
5 10 ( 5 sqrt { 2 } ) ( 5 sqrt { 3 } ) ( 10 sqrt { 2 } )

Explanation:

Step1: Recognize the triangle type

This is a 45 - 45 - 90 triangle. In a 45 - 45 - 90 triangle, the legs are equal, and the hypotenuse \(c\) is related to the leg \(a\) by the formula \(c = a\sqrt{2}\).

Step2: Find the length of side \(BC\)

Since \(\angle A=\angle C = 45^{\circ}\), the triangle \(ABC\) is isosceles. So, \(AB = BC\). Given \(AB=5\sqrt{2}\), then \(BC = 5\sqrt{2}\).

Step3: Find the length of side \(AC\)

Using the formula \(c=a\sqrt{2}\) (where \(a = 5\sqrt{2}\) is the length of the leg). Substitute \(a = 5\sqrt{2}\) into \(c=a\sqrt{2}\), we get \(AC=(5\sqrt{2})\times\sqrt{2}=5\times2 = 10\).

Answer:

\(BC = 5\sqrt{2}\), \(AC = 10\)