Question

Jason and Alison 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''.

Answer 1

`Owl= 67.14ft`

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

`22^(\circ) 8'6'' = 22 + (8)/(60) + (6)/(3600)`

`22^(\circ) 8'6'' = 22.135^(\circ)`

`30^(\circ) 40'30'' = 30 + (40)/(60) + (30)/(3600)`

`30^(\circ) 40'30'' = 30.675^(\circ)`

Considering Jason's position:

`tan(22.135^(\circ)) = (H)/(x + 48)`

Where x = distance between the tree and Alison

Make H the subject

`H = (x + 48)tan(22.135^(\circ))`

Considering Alison's position

`tan(30.675^(\circ)) = (H)/(x)`

Make H the subject

`H = xtan(30.675^(\circ))`

`H = H`

`(x + 48)tan(22.135^(\circ)) = xtan(30.675^(\circ))`

`(x + 48) *0.4068 = x* 0.5932`

Open bracket

`x *0.4068 + 48 *0.4068 = 0.5932x`

`0.4068x + 19.5264 = 0.5932x`

Collect Like Terms

`-0.5932x+0.4068x = -19.5264`

`-0.1864x = -19.5264`

`0.1864x = 19.5264`

Make x the subject

`x = (19.5264)/(0.1864)`

`x = 104.76`

Substitute 104.76 for x in
`H = xtan(30.675^(\circ))`

`H = 104.76 * tan(30.675^(\circ))`

`H = 104.76 * 0.5932`

`H = 62.14`

The above represents the height of the tree.

The height of the owl is:

`Owl= H + 5`

`Owl= 62.14 + 5`

`Owl= 67.14ft`