Question

A Historic monument designed atriangular shape that everyone istrying to visit. The front of it is anequilateral triangle with a perimeterof 18 yards. Someone who is buyingthe monument wants to put asculpture inside of it but first, theymust know the height (altitude) ofthat monument.What is the length of the triangle'saltitude to the nearest tenth of ayard?

Answer 1

If the triangle is equilateral then the length of its sides must be the same. So, each side's length is 6 yards.

Similarly it would have three angles of the same measure, then each angle must be: 180°/3 = 60° as the sum of the three angles of a triangle must be equal to 180°.If the angles are equal each angle would measure one third of 180°.

The formula in this case would be:

`h=\frac{\sqrt[]{3}}{2}a\text{ (a represents the length of one side)}`

Replacing the value of a, we have:

`\begin{gathered} h=\frac{\sqrt[]{3}}{2}\cdot(6)\text{ yards} \\ h=5.196 \\ \text{The answer is 5.2 rounding to the tenth of a yard. } \end{gathered}`