Question

find d.
9√2 yd
45° 45°
d
write your answer in simplest radical form.
□ yards

Explanation:

Step1: Identify the triangle type

The triangle has two \(45^\circ\) angles and a right angle, so it's a 45 - 45 - 90 triangle. In a 45 - 45 - 90 triangle, the legs are equal, and the hypotenuse \(h\) is related to the leg \(l\) by \(h = l\sqrt{2}\).

Step2: Relate hypotenuse and leg

We know the hypotenuse is \(9\sqrt{2}\) yd, and let the leg (which is \(d\)) be \(l\). From the formula \(h=l\sqrt{2}\), we can solve for \(l\) (which is \(d\)):
\[

$$\begin{align*} l\sqrt{2}&=9\sqrt{2}\\ l&=\frac{9\sqrt{2}}{\sqrt{2}}\\ l& = 9 \end{align*}$$

\]

Answer:

9