Question

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

Answer 1

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The altitude divides the triangle into a 30-60-90 triangle. So we can use the 30-60-90 Triangle Theorem to find the altitude. which is: hypotenuse= 2 x shorter leg Longer leg = sqrt(3) x shorter leg

Answer 2

Method 1

Applying the Pythagorean Theorem

we know that

$10^{2}= 5^{2} +a^{2}$

Solve for a

$100= 25 +a^{2}$

$a^{2}=100-25$

$a^{2}=75$

$a=\sqrt{75}=5 \sqrt{3}\ units$

therefore

the answer is

the length of the altitude is $5 \sqrt{3}\ units$

Method 2

we know that

$sin(60\°)=\frac{\sqrt{3}}{2}$ -------> equation A

and

in this problem

$sin(60\°)=\frac{a}{10}$ --------> equation B

equate equation A and equation B

$\frac{\sqrt{3}}{2}=\frac{a}{10}\\\\a=\frac{10\sqrt{3}}{2}\\\\a=5 \sqrt{3}\ units$

therefore

the answer is

the length of the altitude is $5 \sqrt{3}\ units$