Answer:
278.66 feet
Step-by-step explanation:
Since we have the angle ratio of the opposite side to the adjacent side we will be using the trigonometric ratio tangent to solve. We are given the height which represents the opposite side to the sun's angle.
Solving:
[tex]\tan(25^\circ) = \frac{h}{L} ~\text{(h represents height of building, L represents length of shadow)}\\\\\tan(25^\circ) = \frac{130}{L}\\[/tex]
[tex]\[L = \frac{130}{\tan(25^\circ)}\][/tex]
[tex]\[L = \frac{130}{0.4663} \approx \boxed{278.66 \, \text{ft}}\][/tex]
Therefore, the length of the shadow casted by the building is 278.66 feet.
