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?

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

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

y -5 = (-1/4)(x + 8)

step-by-step explanation: