Question

The distance between 2 cell towers is 42 miles. From the western cell tower, a phone signal is 20 degrees north of east and is 48 miles away, how far is this cell phone from the eastern cell tower?

Answer 1

Answer:

48miles

Step-by-step explanation:

The illustration of the scenario is represented in the attached photo

A triangle WEP is formed.

x = distance of the cell phone from the eastern cell tower

The angles in the triangle

= 70 degrees + 70 degrees + 40 degrees = 180degrees

It is not a right angle triangle. This means that we cannot use Pythagoras theorem. We would apply the sine rule which is as follows:

a/sinA = b/sinB = c/since

a, b and c are the sides of the triangle and A,B and C are the corresponding opposite angles to the sides.

Applying it in our triangle,

x/sin 70 = 48/sin70

x = 48sin70/sin70

x = 480 miles

Answer 2

The distance between the cell phone from the eastern tower is approximately 16.7 miles.

Data;

• a = 42 miles
• b = 48 miles
• c = ?
• C = 20°

Cosine Rule

To solve for the distance between the eastern tower from the cell phone, we have to use cosine rule.

$c^2 = a^2 + b^2 -2ab(cosC)$

Let's substitute the values into the equation and solve.

$c^2 = 42^2 + 48^2 -2*42*48cos20\\c^2 = 1764+2304-3788.84\\c^2 = 4068 - 3788.84\\c^2 = 279.16\\c = \sqrt{279.16} \\c = 16.7 mi$

The distance between the cell phone from the eastern tower is approximately 16.7 miles.

Learn more on cosine rule here;

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