Question

note that triangle adb from part a is a 30° - 60° - 90° triangle. drag the tiles to the correct box to show how the pythagorean theorem can be used to find ad. tiles (ad)² + 1² = 2² (ad)² = 3 a² + b² = c² (ad)² + 1 = 4 ad = √3

Explanation:

Step1: Write Pythagorean theorem

$$a^{2}+b^{2}=c^{2}$$

Step2: Substitute values

$$(AD)^{2}+1^{2}=2^{2}$$

Step3: Calculate squares

$$(AD)^{2}+1 = 4$$

Step4: Isolate $(AD)^{2}$

$$(AD)^{2}=3$$

Step5: Solve for $AD$

$$AD=\sqrt{3}$$

Answer:

1. \(a^{2}+b^{2}=c^{2}\)
2. \((AD)^{2}+1^{2}=2^{2}\)
3. \((AD)^{2}+1 = 4\)
4. \((AD)^{2}=3\)
5. \(AD=\sqrt{3}\)