Question

solve for the legs of the 45-45-90 triangle.
triangle image with 45° angle, right angle, hypotenuse 5√2, leg y, leg x
a. x=5 and y=5
b. x = 5 and y = 5√2
c. x = 5√2 and y = 5
d. x = 5√2 and y = 5√2

Explanation:

Step1: Recall 45-45-90 triangle ratios

In a 45-45-90 triangle, the legs are equal, and the hypotenuse \( h \) is related to the leg \( l \) by \( h = l\sqrt{2} \). So, \( l=\frac{h}{\sqrt{2}} \).

Step2: Substitute hypotenuse value

Given hypotenuse \( h = 5\sqrt{2} \), then leg \( l=\frac{5\sqrt{2}}{\sqrt{2}} \).
Simplify: \( \frac{5\sqrt{2}}{\sqrt{2}} = 5 \). Since it's a 45-45-90 triangle, both legs \( x \) and \( y \) are equal, so \( x = 5 \) and \( y = 5 \).

Answer:

a. \( x = 5 \) and \( y = 5 \)