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Chapter 8: Q. 41 (page 528)

Finding the Height of an Airplane An aircraft is spotted by two observers who are 1000 feet apart. As the airplane passes over the line joining them, each observer takes a

sighting of the angle of elevation to the plane, as indicated in the figure. How high is the airplane?

Short Answer

Expert verified

The plane is at a height of approximately 381.69 feet.

Step by step solution

01

Step 1. Given Information

An aircraft is spotted by two observers who are 1000 feet apart.

As the airplane passes over the line joining them, each observer takes a sighting of the angle of elevation to the plane, as indicated in the figure.

Evaluate the angle A formed by the plane using angle sum property of triangle

A=180-40+35A=105慰

02

Step 2. Distance between plane and point Q

psinP=asinAp=sinP脳asinAp=sin40鈭�脳1000sin105鈭�p=0.64脳10000.96p=665.46

03

Step 3. Height of Plane

Now consider right triangle with 胃=35鈭�, the length hopposite to 胃is the height of the plane

sin35鈭�=h665.460.57=h665.46h=381.69

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