Question

18
drag each length to the correct location on the triangle. each length can be used more than once, but not all lengths will be used.
what are the missing side lengths for the triangle?
5 10 $5\sqrt{3}$ $5\sqrt{2}$ $10\sqrt{2}$
(the triangle in the image has a right angle at b, angles at a and c are 45°, and side ab is $5\sqrt{2}$.)

Explanation:

Step1: Identify triangle type

This is a 45-45-90 right triangle, so legs are equal.

Step2: Find length of BC

Leg AB = $5\sqrt{2}$, so leg BC = $5\sqrt{2}$.

Step3: Calculate hypotenuse AC

Use 45-45-90 hypotenuse formula: $\text{Hypotenuse} = \text{leg} \times \sqrt{2}$
$\text{AC} = 5\sqrt{2} \times \sqrt{2} = 5 \times 2 = 10$

Answer:

• Side BC: $5\sqrt{2}$
• Side AC: 10