Answer:
The distance from he ball to the goal is 11.85 feet (Approx) .
Step-by-step explanation:
As given
The angle of elevation from a soccer ball on the ground to the top of the goal is 34° .
If the goal is 8 feet tall.
Now by using the trigonometric identity .
[tex]tan \theta = \frac{Perpendicular}{Base}[/tex]
As shown in the diagram given below
[tex]\theta = 34^{\circ}[/tex]
Perpendicular = AB = 8 feet
Base = BC
Put all the values in the identity .
[tex]tan\ 34^{\circ} = \frac{AB}{BC}[/tex]
[tex]tan\ 34^{\circ} = \frac{8}{BC}[/tex]
[tex]tan\ 34^{\circ} = 0.675\ (Approx)[/tex]
[tex]BC = \frac{8}{0.675}[/tex]
BC = 11.85 feet (Approx)
Therefore the distance from he ball to the goal is 11.85 feet (Approx) .
