Answer:
1419.42 feet
Explanation:
Let y be the height of the blimp above the cars and x₁ be the distance from the blimp to the first car at an angle of depression of 34.99° and x₂ be the distance from the blimp to the second car at an angle of depression of 26.5°.
From trigonometric ratios,
tan34.99° = y/x₁ and tan26.5° = y/x₂
So, x₁ = yt/an34.99° and x₂ = y/tan26.5°
So, the distance between the cars is thus d = x₂ - x₁ = y/tan26.5° - y/tan34.99°= y(1/tan26.5° - 1/tan34.99°) = y(cot26.5° - cot34.99°)
Since y = height of blimp above the road = 2460 feet, substituting it into the equation, we have,
d = 2460(cot26.5° - cot34.99°)
d = 2460(2.0057 - 1.4287)
d = 2460(0.577)
d = 1419.42 feet