What is length of the altitude of the equilateral triangle below?

Accepted Solution

Answer: OPTION D.Step-by-step explanation: Given the equilateral triangle shown in the figure, you need to find the value of the altitude "a". In order to find the altitude, you can use the following Trigonometric Identity: [tex]tan\alpha =\frac{opposite}{adjacent}[/tex] In this case you can identify that: [tex]\alpha=60\Β°\\\\opposite=a\\\\adjacent=2\sqrt{3}[/tex] Therefore, you can substitute values into [tex]tan\alpha =\frac{opposite}{adjacent}[/tex]: [tex]tan(60\Β°)=\frac{a}{2\sqrt{3}}[/tex] Finally, you must solve for the altitude "a". Then, this is: Β [tex](tan(60\Β°))(2\sqrt{3})=a\\\\a=6[/tex] Notice that this result matches with the value shown in Option D.