Question

question 1 of 10
what is the length of (overline{bc}) in the right triangle below?
a. 63
b. (sqrt{63})
c. 15
d. 21
e. 225
f. 3

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \(ABC\) with \(\angle A = 90^{\circ}\), by the Pythagorean theorem \(BC^{2}=AB^{2}+AC^{2}\). Given \(AB = 9\) and \(AC = 12\).
So, \(BC^{2}=9^{2}+12^{2}\).

Step2: Calculate \(BC^{2}\)

\(9^{2}=81\) and \(12^{2}=144\). Then \(BC^{2}=81 + 144=225\).

Step3: Find \(BC\)

Take the square root of \(BC^{2}\), \(BC=\sqrt{225}\). Since \(BC>0\), \(BC = 15\).

Answer:

C. 15