Vectors and magnitude

Question

You are given a vector in xy plane that has a magnitude of 95.0 units and a y component of -55.0 units. What are the two possibilities for its x component?

How do you go about this I dont get it

Answer 1

Solving equation x² + 55² = 95² you will get 2 values for x, that is because the vector can be either in quadrant III or quadrant IV.

Answer 2

go n sleep please

Answer 3

Use the Pythagorean Theorem to find the magnitude:

95^2 = (-55)^2 + x^2

95^2 - (-55)^2 = x^2

The square root of x^2 can be positive or negative, hence the two possible values for x.

95^2 - (-55)^2 = x^2

6000 = x^2

77.5 or -77.5 = x