Question

part iii. 30 - 60 - 90 and 45 - 45 - 90
triangles.
directions: find the value of each variable.
1.
$x=$
$y=$
2.
$x=$
$y=$
3.
$x=$
$y=$

Explanation:

Step1: Analyze the first triangle (45 - 45 - 90 triangle)

In a 45 - 45 - 90 triangle, the legs are equal. So \(x = 10\).
The hypotenuse \(y\) in a 45 - 45 - 90 triangle is \(y=\text{leg}\times\sqrt{2}\). So \(y = 10\sqrt{2}\).

Step2: Analyze the second triangle (30 - 60 - 90 triangle)

In a 30 - 60 - 90 triangle, the hypotenuse is twice the shorter leg. Here, the shorter leg \(x=\frac{32}{2}=16\).
The longer leg \(y=x\sqrt{3}=16\sqrt{3}\).

Answer:

1. \(x = 10\), \(y = 10\sqrt{2}\)
2. \(x = 16\), \(y = 16\sqrt{3}\)