Question

what is the length of (overline{bc}) in the right triangle below?

( bc = 69 )
( bc = 5625 )
( bc = 75 )
( bc = 93 )

Explanation:

Step1: Apply Pythagorean theorem

In a right triangle \(a^{2}+b^{2}=c^{2}\), where \(a = 21\), \(b=72\), and \(c\) is the hypotenuse (\(BC\)).
So, \(BC^{2}=21^{2}+72^{2}\)

Step2: Calculate squares

\(21^{2}=441\), \(72^{2}=5184\)
Then \(BC^{2}=441 + 5184\)

Step3: Sum the values

\(441+5184 = 5625\)

Step4: Find square root

\(BC=\sqrt{5625}\)
\(BC = 75\)

Answer:

BC = 75