Question

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

Answer 1

the actual right answer is c.

Answer 2

The length of the altitude is
`3√(3)` units

Step-by-step explanation

The altitude of a triangle is the vertical height of the triangle.

From the diagram the altitude is
`a`

Method 1: We can use Pythagoras theorem to find
`a`

`6^2=a^2+3^2`

`6^2-3^2=a^2`

`36-9=a^2`

`27=a^2`

We take the square root of both sides,

`√(27)=a`

`√(9*3)=a`

`√(9) * √(3)=a`

`3√(3)=a`

Method 2 Using Trigonometry

`sin(60\degree)=(a)/(6)`

`6sin(60\degree)=a`

`a=6* \frac{√(3)} {2}`

`a=3√(3)`