Question

What is the angle above the x axis (i.e., "north of east") for a vector with components (15 m, 8 m)?

Answer 1

Answer:28.071

Step-by-step explanation:

Given

vector component is (15,8)

i.e. its x component is 15 from origin and y component is 8 m

So angle made by vector with x axis is

$tan\theta =\frac{8}{15}$

$\theta =tan^{-1}\frac{8}{15}$

Answer 2

If you draw out the two components in a head-to-nose fashion, you will create a right angle triangle something like the picture, that is if I interpreted the information right (the way I interpreted it is 15m east and 8m north);
The dotted line represents the x-axis;
Θ represents the desired angle;
Using trigonometry, we can create and solve an equation to get the angle (Θ);
In this case, you can use use sin or cos, I'll go with sin:
SinΘ = opp/hyp
SinΘ = 8/15
Θ = Sin⁻¹(8/15)
= 32.23.... ⇒ 32.2°