Question

find the values of each variable.
$a=\square, b=\square, c=\square, \text{and } d=\square$
(simplify your answers. type exact answers, using radicals as needed.)

Explanation:

Step1: Find side $a$ (45-45-90 triangle)

In a 45-45-90 triangle, legs are equal, and hypotenuse = leg $\times\sqrt{2}$. Rearrange to find leg:
$a = \frac{24\sqrt{2}}{\sqrt{2}} = 24$

Step2: Find side $b$ (30-60-90 triangle)

In a 30-60-90 triangle, hypotenuse = shorter leg $\times2$. Here, shorter leg is $a=24$:
$b = 2 \times 24 = 48$

Step3: Find side $d$ (30-60-90 triangle)

Longer leg = shorter leg $\times\sqrt{3}$. Shorter leg is $a=24$:
$d = 24\sqrt{3}$

Step4: Find side $c$ (45-45-90 triangle)

Legs of 45-45-90 triangle are equal, so $c = a = 24$

Answer:

$a=24$, $b=48$, $c=24$, and $d=24\sqrt{3}$