2. The Pythagorean theorem states:
[tex]c^2=a^2+b^2[/tex]
where a and b are the legs and c is the hypotenuse of a right triangle.
Applying this theorem to triangle AMI (where AI and MA are the legs and MI is the hypotenuse), we get:
[tex]\begin{gathered} MI^2=AI^2+MA^2 \\ MI^2=400^2+100^2 \\ MI^2=160000+10000 \\ MI^2=170000 \\ MI=\sqrt[]{170000} \\ MI\approx412.31\text{ ft} \end{gathered}[/tex]
3. By definition:
[tex]\tan (angle)=\frac{\text{opposite}}{\text{adjacent}}[/tex]
Applying this definition to triangle AMI, considering the angle M, we get:
[tex]\begin{gathered} \tan (\angle M)=\frac{AI}{MA} \\ \tan (\angle M)=\frac{400}{100} \\ \tan (\angle M)=4 \\ \angle M=\arctan (4) \\ \angle M\approx76\text{ \degree} \end{gathered}[/tex]
This angle is greater than 68°, then it satisfies the regulation.
