Question

question 1
10 pts
g.gsr.6.1 (lc)
find the value of x.
image of a right triangle with legs 10, angles 45° and 45°, hypotenuse x
options:
x = 2√10
x = 10
x = 20
x = 10√2

Explanation:

Step1: Identify Triangle Type

The triangle is a right - isosceles triangle (two angles are \(45^{\circ}\), so the two legs are equal, and it's a 45 - 45 - 90 triangle).

Step2: Apply 45 - 45 - 90 Triangle Formula

In a 45 - 45 - 90 triangle, the hypotenuse \(c\) (here \(x\)) is related to the leg \(a\) by the formula \(c=a\sqrt{2}\). Given \(a = 10\), then \(x=10\sqrt{2}\).

Answer:

\(x = 10\sqrt{2}\) (the option with \(x = 10\sqrt{2}\))