Answer:
[tex]Distance = 38.57ft[/tex]
Step-by-step explanation:
Given
[tex]Base = 60[/tex]
[tex]\theta = 50[/tex]
Required
The distance between the top and John
The distance is calculated using:
[tex]sin\alpha = \frac{Distance}{Base}[/tex]
Where
[tex]\alpha = 90 - \theta[/tex] --- the angle between the diagonal line and the vertical line
[tex]\alpha = 90 - 50[/tex]
[tex]\alpha = 40[/tex]
So, we have:
[tex]Sin(40) = \frac{Distance}{60}[/tex]
[tex]Distance = 60 * sin(40)[/tex]
[tex]Distance = 60 * 0.6428[/tex]
[tex]Distance = 38.57ft[/tex]
[tex]Distance = 986 * tan(38)[/tex]
[tex]Distance = 986 * 0.7812[/tex]
[tex]Distance = 770ft[/tex] --- approximated
