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6. An airplane is observed by an air traffic controller at an angle of
elevation of 52°. The airplane is 850 m above the observation deck e
of the tower. What is the distance from the airplane to the tower?
Express your answer to the nearest metre.
control
tower 52°
850 m

We are finding the distance from the plane to the tower, I have marked this as x in the attachment below. Since this is a right triangle and we have an angle, an opposite side, and the hypotenuse, we will use the trigonometry function of sine.

[tex]\dispalystyle sin\theta =\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

Substitute known values:

[tex]\displaystyle sin(52\°) = \frac{850}{x}[/tex]

Multiply both sides of the equation by x:

xsin(52°) = 850

Divide both sides of the equation by sin(52°):

[tex]\displaystyle x= \frac{850}{sin(52\°)}[/tex]

Compute:

x = 1,078.6654828 metres

Round to the nearest metre:

x ≈ 1,079 metres

Apply 6. An airplane is observed by an air traffic controller at an angle of elevation of 52°. The airplane is 850 m above the observation deck e of the tower. What is the distance from the airplane to the tower? Express your answer to the nearest metre. control tower 52° 850 m

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Apply
6. An airplane is observed by an air traffic controller at an angle of
elevation of 52°. The airplane is 850 m above the observation deck e
of the tower. What is the distance from the airplane to the tower?
Express your answer to the nearest metre.
control
tower 52°
850 m