Find the indicated side of the triangle

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

step-by-step explanation:

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step-by-step explanation: