Question

value: 3
solve for the other leg and for the hypotenuse of the 45 - 45 - 90 triangle
45°
u
7
v

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 properties of 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, the two legs are of equal length. Given one leg is 7, so the other leg $v$ has the same length as the given leg. So $v = 7$.

Step2: Use Pythagorean theorem or ratio for hypotenuse

The ratio of the leg to the hypotenuse in a 45 - 45 - 90 triangle is $1:\sqrt{2}$. If the leg length is $a = 7$, then the hypotenuse $u=a\sqrt{2}=7\sqrt{2}$.

Answer:

B. $u = 7\sqrt{2}$ and $v = 7$