The tower is 20 feet above the ground
and the angle of depression is 15 degree
Since Angle of Depression : Any angle form ny the horizontal line and a line to apoint below the line.
So, The figure will be:
We need to find the distance between the suffer and the base of the tower i.e. OB
The line AC is perpendicular to AO
so, angle CAO =90
then : angle CAO = angle BAO + angle BAC
90 = angle BAO + 15
Angle BAO = 90-15
Angle BAO = 75
Now apply the trignometric ratio of Tangent
[tex]\tan \theta=\frac{Perpendicular}{Base}[/tex]here we have angle is BAO
so,
[tex]\begin{gathered} \tan \text{(}\angle\text{BAO)}=\frac{Perpendicular}{Base} \\ \text{tan(}\angle\text{BAO)}=\frac{OB}{OA} \\ OA(\tan \text{(}\angle\text{BAO))}=OB \\ 20(\tan 75)=OB \\ OB=20(\tan 75) \\ OB=20(3.73) \\ OB=74.6 \\ OB=75\text{ ft} \end{gathered}[/tex]Answer :
The surfer from the base of tower is 75 ft away
