Question

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

Answer 1

Answer: 1,079 metres

Step-by-step explanation:

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.

        $\dispalystyle sin\theta =\frac{\text{opposite}}{\text{hypotenuse}}$

Substitute known values:

       $\displaystyle sin(52\°) = \frac{850}{x}$

Multiply both sides of the equation by x:

       xsin(52°) = 850

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

        $\displaystyle x= \frac{850}{sin(52\°)}$

Compute:

        x = 1,078.6654828 metres

Round to the nearest metre:

        x ≈ 1,079 metres