Chapter 8.7, Problem 14WE

To determine

To Find : The value of x that is height of stage level in first balcony.

Answer to Problem 14WE

The value of x that is height of stage level in first balcony is 11.

Explanation of Solution

Given information:

  

The stage of theater, the angle of elevation of the first balcony is 19°, the angle of elevation of the second balcony, 6.3m directly above the first is 29°.

Apply the tan formula in small right angle triangle,

  $\begin{array}{l} \tan x=\frac{\text{Perpendicular}}{\text{Base}}\hfill \\ \tan 19°=\frac{x}{d}\hfill \\ 0.344=\frac{x}{d}\hfill \\ x=0.344d\hfill \end{array}$

Apply the tan formula in big right angle triangle,

  $\begin{array}{l}\tan x=\frac{\text{Perpendicular}}{\text{Base}}\hfill \\ \tan 29°=\frac{6.3+x}{d}\hfill \end{array}$

Further simplify to get

  $\begin{array}{l}0.544=\frac{6.3+0.344d}{d}\hfill \\ 0.544d=6.3+0.344d\hfill \\ 0.2d=6.3\hfill \\ d=31.5\hfill \end{array}$

Therefore, the value of x will be

  $\begin{array}{l}\begin{array}{l}x=0.344d\hfill \\ =0.344\times 31.5\hfill \end{array} \\ =11\end{array}$

Hence, value of x that is height of stage level in first balcony is 11.