Chapter 77, Problem 1A

To determine

To compute the angel of rotation $\angle R$ and angle or tilt $\angle T$.

Answer to Problem 1A

  $\angle R\approx {51}^{\circ }41\text{'}\text{ and }\angle T\approx {54}^{\circ }9\text{'}$.

Explanation of Solution

Given information:

$\angle A={40}^{\circ }38\text{'}$ and $\angle B={47}^{\circ }21\text{'}$.

Calculation:

Applying the formula of $\angle R$ and $\angle T$.

  $\begin{array}{l}\tan \angle R=\frac{\tan \angle B}{\tan \angle A}\\ \tan \angle R=\frac{\tan {47}^{\circ }21\text{'}}{\tan {40}^{\circ }38\text{'}}\\ \tan \angle R=\frac{1.086}{0.858}\\ \angle R={\tan }^{-1}(1.266)\\ \angle R\approx {51}^{\circ }41\text{'}\\ \\ \tan \angle T=\sqrt{{\tan }^2\angle A+{\tan }^2\angle B}\\ \tan \angle T=\sqrt{{\tan }^2{40}^{\circ }38\text{'}+{\tan }^2{47}^{\circ }21\text{'}}\\ \tan \angle T=\sqrt{0.736+1.180}\\ \tan \angle T=\sqrt{1.916}\\ \tan \angle T=1.384\\ \angle T={\tan }^{-1}(1.384)\\ \angle T\approx {54}^{\circ }9\text{'}\end{array}$