Question

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

Answer 1

the actual right answer is c.

Answer 2

ANSWER

The length of the altitude is $3\sqrt{3}$ units

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,

$\sqrt{27}=a$

$\sqrt{9\times3}=a$

$\sqrt{9} \times \sqrt{3}=a$

$3\sqrt{3}=a$

Method 2 Using Trigonometry

$sin(60\degree)=\frac{a}{6}$

$6sin(60\degree)=a$

$a=6\times \frac{\sqrt{3}} {2}$

$a=3\sqrt{3}$