Answer:
7√2
Step-by-step explanation:
Knowing that the angle is 45° (or π/4 radians) and the opposite leg has a length of 7, you can find the length of b with:
7 / b = sin(π / 4)
7 / (sin(π / 4)) = b
b = 7 / (1 / √2)
b =7√2
A simpler way to get the answer is to note that a right triangle with one 45° angle must be an isoceles right triangle, so both legs are the same length. Using the Pythagorean Theorem:
a² + 7² = b²
Since we know a = 7,
7² + 7² = b²
b = √(2 * 49)
b = 7√2
