Chapter 4, Problem 84RE

(a)

To determine

To Draw:A right triangle

Explanation of Solution

Given information: Anescalator $152feet$

in length rises to a platform and makes ${30}^{\circ }$ angle with the ground

Calculation:

  $\omega =$ height of the platform above the ground

(b)

To determine

To Find:Trigonometric function to write an equation involving the unknown quantity

Answer to Problem 84RE

  $\sin {30}^{\circ }=\frac{\omega }{152}$

Explanation of Solution

Given information: Anescalator $152feet$ in length rises to a platform and makes ${30}^{\circ }$ angle with the ground

Concept used: Let $\theta$ be an acute angle of a right triangle. The six trigonometric functions of the angle $\theta$ are defined as follows

  $\sin \theta =\frac{opp}{hyp}$

The abbreviations opp, adj, and hyp represent the length of the three sides of a right triangle

  $opp=$ the length of the side opposite $\theta$

  $adj=$ the length of the side adjacent to $\theta$

  $hyp=$ the length of the hypotenuse

Calculation:

Only hypotenuse and the opposite side are given

  $\sin \theta =\frac{opp}{hyp}$

  $\begin{array}{l}\theta ={30}^{\circ }\\ opp=\omega \\ hyp=152\end{array}$

  $\sin {30}^{\circ }=\frac{\omega }{152}$

(c)

To determine

To Find:Height of the platform above the ground

Answer to Problem 84RE

Height of the platform above the ground $=76$

Explanation of Solution

Given information: Anescalator $152feet$ in length rises to a platform and makes a ${30}^{\circ }$ angle with the ground

Concept used: Let $\theta$ be an acute angle of a right triangle. The six trigonometric functions of the angle $\theta$ are defined as follows

  $\sin \theta =\frac{opp}{hyp}$

The abbreviations opp, adj, and hyp represent the length of the three sides of a right triangle

  $opp=$ the length of the side opposite $\theta$

  $adj=$ the length of the side adjacent to $\theta$

  $hyp=$ the length of the hypotenuse

Calculation:

Only hypotenuse and the opposite side are given

  $\sin \theta =\frac{opp}{hyp}$

  $\begin{array}{l}\theta ={30}^{\circ }\\ opp=\omega \\ hyp=152\end{array}$

  $\sin {30}^{\circ }=\frac{\omega }{152}$

  $\frac{1}{2}=\frac{\omega }{152}$

  $\omega =76$