Question

4. Jason and Allison are hiking in the woods when they spot a rare owl in a tree. Jason stops and measures an angle of elevation of 22^ 8^ prime ^ prime prime . At the same time Allison is standing 48 feet closer to the tree, measuring an angle of elevation of 30^ 40^ prime ' 30" to the owl If Jason and Allison are the same height, their eyes 5 feet from the ground , find the height of the owl in the tree .

Answer 1

Here is the correct format for the question.

Jason and Allison are hiking in the woods when they spot a rare owl in a tree. Jason stops and measures an angle of elevation of 22° 8’ 6”. At the same time, Allison is standing 48 feet closer to the tree, measuring an angle of elevation of 30° 40’ 30” to the owl. If Jason and Allison are the same height, their eyes 5 feet from the ground, find the height of owl in the tree.

Answer:

The height of the owl from the ground is: 67.1337  ft

Step-by-step explanation:

The first step we are meant to start with is by convert our angle of elevation into degree;

So; we have the given data

22° 8’ 6”

30° 40’ 30”

To degrees ; we get :

$22^o\, 8' \,6" = 22 +\frac{8}{60} +\frac{6}{3600}=22.135^o\\ \\ 30^o\, 40' \,30" = 30 +\frac{40}{60} +\frac{30}{3600}=30.675^o$

From the attached file below; we can see a diagrammatic representation of the two right angle triangles together showing the data set which include the position of the hikers , the owl on the tree and the angle of elevations.

The trigonometric equations derived from the right angled triangle can be illustrated as:

$tan(22.135^o)=\frac{T}{48+x} \\ \\tan(30.675^o)=\frac{T}{x}$

From above equation ;

solving for the value of T , then equating both equations to determine the value of x to find the  the height of the owl in the tree; we have:

$T=(48+x)\,tan(22.135^o)\\ \\T=x\,\,tan(30.675^o)\\ \\(48+x)\,tan(22.135^o)=x\,\,tan(30.675^o)\\ \\ 48\,tan(22.135^o)+x\,\,tan(22.135^o)=x\,\,tan(30.675^o)\\ \\ 48\,tan(22.135^o)=x\,\,(tan(30.675^o)-tan(22.135^o))\\ \\ x=\frac{48\,tan(22.135^o)}{tan(30.675^o)-tan(22.135^o)} \\ \\x=104.75\,\,ft$

However; to find T; we have:

$T-x\,\,tan(30.675^o)\\ \\ T=(104.75\,ft)\,\,tan(30.675^o)\\ \\ T=62.1337\,\,ft$

From the question; if we take an integral look and an in depth understanding of the question; we will realize that  the value of T = 62.1337 ft is the height the owl is relative to the eye level of the hikers; so if we want to determine  the height of the owl from the ground, there is need to add the given (5 feet from the ground)  to this number:

SO;

The height of the owl from the ground is:  (62.1337 + 5) ft

= 67.1337  ft