We are given the following right triangle:
The diagram shows a right triangle with a hypotenuse of 16 and a shorter side of 8. The angles are 30 -60 - 90. The shorter side is in front of the smaller angle. We can use the Pythagorean theorem to determine the length of the missing side:
[tex]h^2=a^2+b^2[/tex]Where "h" is the hypotenuse, "a" and "b" are the sides. Substituting we get:
[tex]16^2=8^2+x^2[/tex]Now, we solve the squares:
[tex]256=64+x^2[/tex]now, we subtract 64 from both sides:
[tex]\begin{gathered} 256-64=x^2 \\ 192=x^2 \end{gathered}[/tex]Now, we take the square root to both sides:
[tex]\begin{gathered} \sqrt{192}=x \\ 13.86=x \end{gathered}[/tex]Therefore, the value of the missing side is 13.86
