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3 years ago

A blimp is flying parallel to a road and is 2460 feet directly above it. The angles of depression of two parked

Mathematics

1 answer:

Nina [5.8K]3 years ago

4 0

Answer:

‭1419.42‬ feet

Step-by-step 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

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