Question

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

Answer 1

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=√(75)=5 √(3)\ units`

therefore

the answer is

the length of the altitude is
`5 √(3)\ units`

Method 2

we know that

`sin(60\°)=(√(3))/(2)` -------> equation A

and

in this problem

`sin(60\°)=(a)/(10)` --------> equation B

equate equation A and equation B

`(√(3))/(2)=(a)/(10)\\\\a=(10√(3))/(2)\\\\a=5 √(3)\ units`

therefore

the answer is

the length of the altitude is
`5 √(3)\ units`