Chapter 4.8, Problem 27E

To determine

To find: An equation involving the unknown distance and then to find the distance between the roof and the drone.

Answer to Problem 27E

The equation involving the unknown distance is $d=25(\tan 21.5°-\tan 15°)$ and the distance between the roof and the drone is $3.149mt.$

Explanation of Solution

Given information:

Distance of point from the office building $=25mt.$

Angle of elevation to the roof $=15°$

Angle of elevation to hovering drone $=21°30\text{'}$

Calculation:

  $21°30\text{'}={\left(21+\frac{30}{60}\right)}^{°}=21.5°$

Let distance between the roof and drone $=d$

and height of building $=a$

  

From figure,

  $\begin{array}{l}\tan 15°=\frac{a}{25}\\ \Rightarrow a=25\tan 15°-(i)\\ \&\\ \tan 21.5°=\frac{a+d}{25}\\ \Rightarrow a+d=25\tan 21.5°-(ii)\\ \\ (ii)-(i),\\ \\ d=25\tan 21.5°-25\tan 15°\\ d=25(\tan 21.5°-\tan 15°)\\ \\ \end{array}$

Thus, the equation involving the unknown distance is $d=25(\tan 21.5°-\tan 15°)$ .

The distance between the roof and the drone $=25(0.3939-0.268)$

  $\begin{array}{l}=25(0.126)\\ =3.149mt.\end{array}$