The diagram shows the coordinates of the vector. They are:
East-coordinate = 6
North-coordintate = 4
A) To find the magnitude you just use Pythagorean theorem:
c^2 = 6^2 + 4^2 = 36 + 16 = 52 => c = √52 = 7.21
7.21 rounded to the nearest tenth is 7.2
B) To find the direction find the angle using trigonometric ratios:
tan(angle) = 4/6 = 2/3 => angle = arctan(2/3) = 33.69 degrees
That is 33.69 degrees North of East, which is written N 33.69° E
Draw an equilateral triangle FGH so that FH is the horizontal base. Draw a vertical line GR from G to line FH to represent the height of the triangle.
Let a = length of a side of the equilateral triangle (all sides are equal).
Each angle is 60° because the three angles add up to 180°.
Let h = GR, the height of the triangle.
Because the triangle is equilateral, triangle FGR is a right triangle, with
m∠F = 60° ,
m∠R = 90°,
FG = a.
By definition,
sin(F) = h/a
That is,
h = a*sin(F) = a*sin(60) = a*(√3/2).
Answer:
The height of the equilateral triangle is (a/2)√3,
where a = length of a side of the triangle.
