Answer:
[tex]Owl= 67.14ft[/tex]
Step-by-step explanation:
See comment for complete question.
The given information is represented in the attached figure.
First convert 22°8'6'' and 30° 40’ 30” to degrees
[tex]22^{\circ} 8'6'' = 22 + \frac{8}{60} + \frac{6}{3600}[/tex]
[tex]22^{\circ} 8'6'' = 22.135^{\circ}[/tex]
[tex]30^{\circ} 40'30'' = 30 + \frac{40}{60} + \frac{30}{3600}[/tex]
[tex]30^{\circ} 40'30'' = 30.675^{\circ}[/tex]
Considering Jason's position:
[tex]tan(22.135^{\circ}) = \frac{H}{x + 48}[/tex]
Where x = distance between the tree and Alison
Make H the subject
[tex]H = (x + 48)tan(22.135^{\circ})[/tex]
Considering Alison's position
[tex]tan(30.675^{\circ}) = \frac{H}{x}[/tex]
Make H the subject
[tex]H = xtan(30.675^{\circ})[/tex]
[tex]H = H[/tex]
[tex](x + 48)tan(22.135^{\circ}) = xtan(30.675^{\circ})[/tex]
[tex](x + 48) *0.4068 = x* 0.5932[/tex]
Open bracket
[tex]x *0.4068 + 48 *0.4068 = 0.5932x[/tex]
[tex]0.4068x + 19.5264 = 0.5932x[/tex]
Collect Like Terms
[tex]-0.5932x+0.4068x = -19.5264[/tex]
[tex]-0.1864x = -19.5264[/tex]
[tex]0.1864x = 19.5264[/tex]
Make x the subject
[tex]x = \frac{19.5264}{0.1864}[/tex]
[tex]x = 104.76[/tex]
Substitute 104.76 for x in [tex]H = xtan(30.675^{\circ})[/tex]
[tex]H = 104.76 * tan(30.675^{\circ})[/tex]
[tex]H = 104.76 * 0.5932[/tex]
[tex]H = 62.14[/tex]
The above represents the height of the tree.
The height of the owl is:
[tex]Owl= H + 5[/tex]
[tex]Owl= 62.14 + 5[/tex]
[tex]Owl= 67.14ft[/tex]
