Question

find d.
right triangle with right angle, 30° angle, 60° angle, hypotenuse labeled 40√2 in, side adjacent to 30° angle labeled d
write your answer in simplest radical form.
blank inches

Explanation:

Step1: Identify cosine of 30°

$\cos(30^\circ) = \frac{d}{40\sqrt{2}}$

Step2: Substitute $\cos(30^\circ)$ value

$\cos(30^\circ) = \frac{\sqrt{3}}{2}$, so $\frac{\sqrt{3}}{2} = \frac{d}{40\sqrt{2}}$

Step3: Solve for d

$d = 40\sqrt{2} \times \frac{\sqrt{3}}{2} = 20\sqrt{6}$

Answer:

$20\sqrt{6}$ inches