If the sides of a rectangular solid are as shown,and $s = 4$ ,determine the angle,?,between the diagonal of the base of the solid and the diagonal of the solid.Round answer to two decimal places. A)21.91^o B)24.09^o C)17.21^o D)26.28^o E)19.86^o

Question

Quizplus · Accepted Answer

First, we can use the Pythagorean theorem to find the diagonal of the base of the solid:
$BD = \sqrt{8^2 + 11^2} = \sqrt{185}$

Next, we can use the Pythagorean theorem to find the diagonal of the solid itself:
$AD = \sqrt{8^2 + 11^2 + 11^2} = \sqrt{280}$

Finally, we can use the dot product to find the angle between these two vectors:
$\cos	heta = \frac{\vec{AB}\cdot\vec{BC}}{\left|\vec{AB}ight|\left|\vec{BC}ight|} = \frac{BD^2}{AD\cdot BD} = \frac{\sqrt{185}}{\sqrt{280}}$

Using a calculator, we can find that $\cos	heta \approx 0.866$, and thus $	heta \approx 24.09^\circ$ (rounded to two decimal places).

Therefore, the correct answer is B.

If the Sides of a Rectangular Solid Are as Shown,and s=4s = 4s=4

If the Sides of a Rectangular Solid Are as Shown,and $s = 4$