A blimp is 1600 meters high in the air and measures the angles of depression to two stadiums to the east of the blimp. if those

Question

2 years ago

5

measurements are 71.7° and 25.2°, how far apart are the two stadiums?

1 answer:

Sonja [21] · Answer 1 · 2023-06-09T11:23:34+03:00

The two stadiums are 2,871 meters

A blimp = point A

stadium 1 = point B

stadium 2 = point C

height of the blimp , AD = 1600

depression angle of stadium 1 , ∠y = 71.7°

depression angle of stadium 2 , ∠x = 25.2°

distance between the two stadiums = d

So, it forms 2 triangles ABD and ACD,

Using the trigonometric ratios,

tan θ = Altitude / Base

DC = AD × tan (90° - x)

= 1600 × tan( 90° - 25.2° )

= 1600 × cot(25.2°)

= 1600 × 2.13

DB = AD × tan (90° - y)

= 1600 × tan( 90° - 71.7° )

= 1600 × cot(71.7°)

= 1600 × 0.33

∴ d = DC - DB

= 1600 * [ tan( 90° - 25.2° ) - tan( 90° - 71.7° ) ]

= 2,871 meters

To learn more about angle of depression from the given link

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