A plane is observed to be approaching the airport. It is at a distance of 10 km from the point of observation and makes an angle of elevation of 67.5°. What is the height of the plane above the ground?
A.10√(2+√2) km
B.10√(2-√2) km
C.5√(2+√2) km
D.5√(2-√2) km✓ Correct
Explanation
Height = 10 sin 67.5°. sin 67.5° = cos 22.5° = √((1+cos 45°)/2) = √((1+√2/2)/2) = √((2+√2)/4) = √(2+√2)/2. So height = 10 · √(2+√2)/2 = 5√(2+√2). This is option (c). Note: Verifying — sin 67.5° = √(2+√2)/2, so height = 5√(2+√2) km, option (c).
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