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A blimp can be seen flying at an altitude of 5500 feet above a motor speedway during a race. The slanted distance directly to the pagoda at the startdashfinish line is d feet. Express the horizontal distance h as a function of d.

1 Answer

1 vote

Answer:

The expression of h as function of x is h =
√((d + 5500) (d - 5500))

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 =
(AC)/(BC) =
(h)/(d)

And sin Ф =
(AB)/(BC) =
(5500)/(d)

∵, cos²Ф = 1 - sin²Ф

So,
((h)/(d))^(2) =
1 - ((5500)/(d))^(2)

Or,
((h)/(d))^(2) =
((d^(2)- 5500^(2))/(d^(2)))

Or, h² = d² - 5500²

∴ h =
\sqrt{d^(2)- 5500^(2)}

Or, h =
√((d + 5500) (d - 5500))

Hence The expression of h as function of x is h =
√((d + 5500) (d - 5500)) Answer

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