Chapter 4.8, Problem 23E

To determine

Tofind: The Height of steeple using trigonometric ratio.

Answer to Problem 23E

The height of the steeple is 19.89ft.

Explanation of Solution

Given:

the height of the steeple and the angles of elevation to D and A are ${35}^0$ and $4740^{\prime }$ respectively.

Concept used:

  $\text{tanθ=}\frac{\text{perpendicular}}{\text{base}}$ it doesn’t depend on hypotenuse.

Calculation:

The figure can be drawn as a right-angled triangle as shown below.

Where AD is the height of the steeple and the angles of elevation to D and A are ${35}^0$ and $4740^{\prime }$ respectively.

Use the fact that BC=50 ft.

In the right angle $\Delta \text{DBC}$ right angled at B, for the smaller triangle used the fact that;

  $\tan {35}^0=\frac{\text{BD}}{\text{BC}}$

  $\text{BD=50tan35}$

  $\text{BD=35}\text{.01ft}$

For the larger triangle use the fact that in the right $\Delta \text{ABC}$

  ${\text{θ=47}}^{0}40^{\prime }$

  $\text{θ=47}\text{.6<msup><mo>6</mo><mo>′</mo></msup>}$

  $\text{tan47}\text{.66=}\frac{\text{AB}}{\text{BC}}$

  $\text{AB=50tan47}\text{.86}$

  $\Rightarrow \text{54}\text{.87ft}$

Now the height of steeple is given as

  $\text{AB-BD=AD}$

  $\text{AD=54}\text{.87-35}\text{.01}$

  $\text{AD=19}\text{.89ft}$

Therefore, the height of the steeple is 19.89ft.