Question

Question 4

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 the angle, 0, between your line of sight to the first tower and the
highway to the nearest tenth of a degree. (A calculator is needed for this question) LOOKING FOR LINE OF SIGHT

Answer 1

Answer: 24.6 degrees.

Step-by-step explanation: To determine the angle, we need to first draw a diagram:

T1 x

*------|--------*

| θ

|

|

|

|

|

*------|--------*

T2 x

Let θ be the angle between the line of sight from the phone to tower 1 and the highway.

We can use the tangent function to find θ:

tan θ = (height of tower 1 - height of phone) / (distance from tower 1 to phone)

The height of tower 1 is not given, but we can use the fact that the towers are 6000 feet apart and that the phone is north of the highway to find the height difference between tower 1 and the phone. Let h be the height difference:

h = sqrt((distance between towers)^2 - (distance from tower 1 to tower 2)^2) / 2

= sqrt(6000^2 - 2420^2) / 2

≈ 5415.5 feet

Now we can find θ:

tan θ = (h - 12) / 5050

θ ≈ tan^-1((h - 12) / 5050)

≈ 24.6 degrees

Therefore, the angle between the line of sight from the phone to tower 1 and the highway is approximately 24.6 degrees.