Answer:
[tex]h=50.25\ ft[/tex]
Step-by-step explanation:
Right Triangles
In a right triangle, one of the internal angles is 90°. When this happens, there is always a longer side, called hypotenuse and two shorter sides, called legs. They relate to Pythagoras's theorem. The basic trigonometric relations also stand, including
[tex]\displaystyle tan\alpha=\frac{a}{c}[/tex]
where a is the opposite leg to [tex]\alpha[/tex] and c is its adjacent led .
In our problem, we have a statue being looked by a person in such a way that the top of the statue forms an angle of 8° with the horizontal and the base of the statue forms an angle of 14° down. We also know the distance from the person to the statue is 50 ft. The situation is shown in the image below.
The height of the statue is h=a+b, where
[tex]a=50tan8^o[/tex]
[tex]b=50tan14^o[/tex]
Thus
[tex]h=50tan8^o+50tan14^o[/tex]
[tex]h=50(tan8^o+tan14^o)[/tex]
[tex]\boxed{h=50.25\ ft}[/tex]
