Chapter 14.3, Problem 18PPSE

Solution

a.

To find: The height of the flagpole to the nearest foot.

The height of the flagpole is $299.88ft.$

Given:

The figure is given below:

  

Where the angle of elevation of the sun was ${55}^{•}$ and the length of the shadow cast by this flagpole was $\text{210}\text{ft}\text{.}$

Calculation:

Here, the height of the flagpole $\left(AB\right)$ is given as:

  $\begin{array}{c}\tan C=\frac{AB}{BC}\\ \tan {55}^{•}=\frac{AB}{210}\\ AB=1.428\times 210\\ AB=299.88\end{array}$

Hence, the height of the flagpole is $\text{299}\text{.88}\text{ft}\text{.}$

b.

To determine the length of the shadow when the angle of elevation of the sun was ${34}^{•}.$

The length of the shadow is $\text{444}\text{.266}\text{ft}\text{.}$

Given:

The figure is given below:

  

Calculation:

The length of the shadow $\left(EF\right)$ is given as:

  $\begin{array}{c}\text{tan}F\text{=}\frac{\text{DF}}{\text{EF}}\\ {\text{tan34}}^{\text{•}}\text{=}\frac{\text{299}\text{.88}}{\text{EF}}\\ \text{EF=}\frac{\text{299}\text{.88}}{\text{0}\text{.675}}\\ \text{EF=444}\text{.266}\end{array}$

Hence, the length of the shadow is $\text{444}\text{.266}\text{ft}\text{.}$

a.

To find: The assuming quantity for the flagpole and the shadow to solve the problems.

Angle of elevation of the sun

Interpretation:

Here, the problem can be solved if the angle of elevation of the sun is assumed.

With respect to the angle, the length of opposite and adjacent legs can be found using tangent function.