Question

solve for the other leg and for the hypotenuse of the 45 - 45 - 90 triangle. a. u = 7 and v = 7 b. u = 7 and v = 7\sqrt{2} c. u = 7\sqrt{2} and v = 7 d. u = 7\sqrt{2} and v = 7\sqrt{2}

Explanation:

Step1: Recall 45 - 45 - 90 triangle property

In a 45 - 45 - 90 triangle, the two legs are of equal length. Given one leg is 7, so the other leg \(v = 7\).

Step2: Use Pythagorean theorem for hypotenuse

For a right - triangle \(a^{2}+b^{2}=c^{2}\). In a 45 - 45 - 90 triangle with legs \(a = b=7\), then \(c=\sqrt{7^{2}+7^{2}}=\sqrt{49 + 49}=\sqrt{98}=7\sqrt{2}\), so \(u = 7\sqrt{2}\).

Answer:

C. \(u = 7\sqrt{2}\) and \(v = 7\)