Question

On many cell phones with GPS, an approximate location can be given before the GPS signal is received. This is done by a process called triangulation, which works by using the distance from two known points. Suppose there are two cell phone towers within range of you, located 6000 feet apart along a straight highway that runs east to west, and you know you are north of the highway. Based on the signal delay, it can be determined you are 5050 feet from the first tower, and 2420 feet from the second. Determine your position north and east of the first tower, θ , to the nearest tenth of a degree. (A calculator is needed for this question)

Answer 1

Answer

• 23.32°
• x=4637.16 feet
• y=1999.8 feet  
• Explanation

Sketch a triangle ABC, where A is at the apex(top) and BC is the base.Let side AB=5050 feet and BC=6000feet.Drop a perpendicular line from A to BC at O to represent distance y and OB is distance x.

Point A = your location

Point B=First tower and Point C is the second tower.

To calculate the angle in degrees we use law of cosines,

2420²=5050²+6000²-(2)(5050)(6000)(cosB)

B=23.32° is the angle in question

Secondly, we find value of x

CosB=x/5050

X=4637.16feet, the position east of the tower

Thirdly, we calculate y

SinB=y/5050

0.39599=y/5050

y=1999.77

y=1999.8 feet , the position north of the tower