Respuesta :
Answer:
The expression of h as function of x is h = [tex]\sqrt{(d + 5500) (d - 5500)}[/tex]
Step-by-step explanation:
Given as :
The distance of blimp (AB) = 5500 feet
The slanted distance to the pagoda (BC) = d feet
The horizontal distance (AC) = h
Let the angle made between slanted distance and horizontal distance be Ф
So , cos Ф = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{h}{d}[/tex]
And sin Ф = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{5500}{d}[/tex]
∵, cos²Ф = 1 - sin²Ф
So, [tex](\frac{h}{d})^{2}[/tex] = [tex]1 - (\frac{5500}{d})^{2}[/tex]
Or, [tex](\frac{h}{d})^{2}[/tex] = [tex](\frac{d^{2}- 5500^{2}}{d^{2}})[/tex]
Or, h² = d² - 5500²
∴ h = [tex]\sqrt{d^{2}- 5500^{2}}[/tex]
Or, h = [tex]\sqrt{(d + 5500) (d - 5500)}[/tex]
Hence The expression of h as function of x is h = [tex]\sqrt{(d + 5500) (d - 5500)}[/tex] Answer
