Question

b = 4; c = 2√2
b = 2√2; c = 2√2
b = 2; c = 4
b = 4; c = 4√2

Explanation:

Step1: Determine the value of \( b \)

In a right - angled triangle with angles \( 45^{\circ},45^{\circ},90^{\circ} \), the legs are equal. Since one leg is \( 4 \), then \( b = 4 \).

Step2: Calculate the value of \( c \)

Using the Pythagorean theorem \( c=\sqrt{b^{2}+4^{2}} \). Substitute \( b = 4 \) into the formula: \( c=\sqrt{4^{2}+4^{2}}=\sqrt{16 + 16}=\sqrt{32}=4\sqrt{2} \)

Answer:

\( b = 4;c = 4\sqrt{2} \) (the fourth option)