Question

if ( a = 6 ) and ( b = 8 ), what is the length of ( c ) in a right triangle?
a. 12
b. 10
c. 8
d. 14

Explanation:

Step1: Apply Pythagorean theorem

$$a^{2}+b^{2}=c^{2}$$

Step2: Substitute values

Given \(a = 6\) and \(b = 8\), substitute into the formula:
$$6^{2}+8^{2}=c^{2}$$
$$36 + 64=c^{2}$$
$$100=c^{2}$$

Step3: Solve for \(c\)

Take the square root of both sides:
$$c=\sqrt{100}$$
$$c = 10$$

Answer:

B. 10