An observer (O) spots a plane (P) taking off from a local airport and flying at a 33° angle
1 answer:
Answer: 10,779 feets
Step-by-step explanation:
From the sketch attached ;
∠POT is the Angle of elevation = 33°
Height of tower = 7000 Feets
Taking the triangle POT
WHERE PT = 7000 Feets (Opposite)
Distance (d) between the bird and plane is the ADJACENT,
NOTE: (BP = OT = d)
Taking the tangent of the angle of elevation;
Tan Θ = opposite / Adjacent
Tan 33° = 7000 / d
Cross multiply
d × 0.6494075 = 7000
d = 7000 / 0.6494075
d = 10779.054 = 10,779 feets
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<span>EF^2 = 16 + 1 = 17. </span>
<span>DF^2 = 9 + 25 = 34. </span>
<span>Since (DE)^2 + (EF)^2 = (DF)^2,
</span><span> angle E is 90 degrees.
</span><span> DF must be the hypotenuse
</span>see attachment below
<span>EF^2 = 16 + 1 = 17. </span>
<span>DF^2 = 9 + 25 = 34. </span>
<span>Since (DE)^2 + (EF)^2 = (DF)^2,
</span><span> angle E is 90 degrees.
</span><span> DF must be the hypotenuse
</span>see attachment below