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 \(5 \sqrt{3}\ units\)
