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
measurements are 71.7° and 25.2°, how far apart are the two stadiums?
A. 3929 m
B. 3327 m
C. 3150 m
D. 2871 m
A. 3929 m
B. 3327 m
C. 3150 m
D. 2871 m
1 answer:
The explanation of the problem is as shown in the figure.
<span>A blimp ⇒⇒⇒ point A
</span><span>stadium 1 ⇒⇒⇒ point B
</span><span>stadium 2 ⇒⇒⇒ point C
height of the blimp ⇒⇒⇒ AD = 1600
</span>depression angle of <span>stadium 1 ⇒⇒⇒ ∠y = </span><span>71.7°
</span>depression angle of <span>stadium 2 ⇒⇒⇒ ∠x = 25.2°
distance between </span><span><span>the two stadiums ⇒⇒⇒ d
DC = AD * tan (90° - x) = 1600 * tan( 90° - 25.2° )
DB = AD * tan (90° - y) = 1600 * tan( 90° - 71.7° )
</span></span>∴ d = DC - DB
= 1600 * [ tan( 90° - 25.2° ) - <span>tan( 90° - 71.7° ) ]
= 2,871 </span><span>meters
</span>∴ The correct choice is option (D)
<span>A blimp ⇒⇒⇒ point A
</span><span>stadium 1 ⇒⇒⇒ point B
</span><span>stadium 2 ⇒⇒⇒ point C
height of the blimp ⇒⇒⇒ AD = 1600
</span>depression angle of <span>stadium 1 ⇒⇒⇒ ∠y = </span><span>71.7°
</span>depression angle of <span>stadium 2 ⇒⇒⇒ ∠x = 25.2°
distance between </span><span><span>the two stadiums ⇒⇒⇒ d
DC = AD * tan (90° - x) = 1600 * tan( 90° - 25.2° )
DB = AD * tan (90° - y) = 1600 * tan( 90° - 71.7° )
</span></span>∴ d = DC - DB
= 1600 * [ tan( 90° - 25.2° ) - <span>tan( 90° - 71.7° ) ]
= 2,871 </span><span>meters
</span>∴ The correct choice is option (D)
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