Chapter 77, Problem 1A

To determine

(a)

To sketch and label a rectangular solid and pyramid formed by the rectangular surface edges and show the right triangle that contain all the angles.

Answer to Problem 1A

  

Explanation of Solution

Given information:

The top, front and right side views of a part are shown in the following figure-

  

Calculation:

On the basis of the given information $EACB$ is the obtained pyramid and $△ECD$ is the right triangle obtained which is right angled at $D$.

  

To determine

(b)

To compute the angle $\angle R$.

Answer to Problem 1A

  $\angle R\approx {22}^{\circ }40\text{'}$.

Explanation of Solution

Given information:

Given $\angle A={32}^{\circ }20\text{'}$ and $\angle B={56}^{\circ }35\text{'}$.

Calculation:

Applying the formula of $\angle R$.

  $\begin{array}{l}\tan \angle R=\frac{\tan \angle A}{\tan \angle B}\\ \tan \angle R=\frac{\tan {32}^{\circ }20\text{'}}{\tan {56}^{\circ }35\text{'}}\\ \tan \angle R=0.418\\ \angle R={\tan }^{-1}(0.418)\\ \angle R\approx {22}^{\circ }40\text{'}\end{array}$

To determine

(c)

To compute the angle $\angle C$.

Answer to Problem 1A

  $\angle C\approx {30}^{\circ }17\text{'}$.

Explanation of Solution

Given information:

Given $\angle A={32}^{\circ }20\text{'}$ and $\angle B={56}^{\circ }35\text{'}$.

Calculation:

Applying the formula of $\angle C$.

  $\begin{array}{l}\cot \angle C=\sqrt{{\cot }^2\angle A+{\cot }^2\angle B}\\ \cot \angle C=\sqrt{{\cot }^2{32}^{\circ }20\text{'}+{\cot }^2{56}^{\circ }35\text{'}}\\ \cot \angle C=\sqrt{2.496+0.435}\\ \cot \angle C=\sqrt{2.931}\\ \cot \angle C=1.712\\ \angle C={\cot }^{-1}(1.712)\\ \angle C\approx {30}^{\circ }17\text{'}\end{array}$