# Math Help - Trigonometry with vectors

1. ## Trigonometry with vectors

Jack walks x km on a bearing of 100 degrees from O, then y km on a bearing of 200 degrees to H. Calculate the magnitude and direction of the displacement vector OH when:

a) x=6, y=7
b) x=6, y=10

The answer to a) should be 8.4 KM, 155 degrees. And b) should be 10.7 km, 167 degrees, but I can't get these answers. Please help.

2. Originally Posted by tory88
Jack walks x km on a bearing of 100 degrees from O, then y km on a bearing of 200 degrees to H. Calculate the magnitude and direction of the displacement vector OH when:

a) x=6, y=7
b) x=6, y=10

The answer to a) should be 8.4 KM, 155 degrees. And b) should be 10.7 km, 167 degrees, but I can't get these answers. Please help.
This formula:
$H_x = x \cos(100) + y \cos(200)$
$H_y = x \sin(100) + y \sin(200)$

with the data given for a:
$H_x = 6 \cos(100) + 7 \cos(200)$
$H_y = 6 \sin(100) + 7 \sin(200)$

magnitude = $\sqrt{ H_x^2 + H_y^2}$

direction = ArcTangent $\left(\dfrac{H_y}{H_x} \right)$

When computing the arctan you need to know the quadrant:
Quadrant 1 or 3 & Quadrant 2 or 4 and adjust the results accordingly.