Answer:
4.2 km
Explanation:
A triangle is a polygon with three sides and three angles. There are different types of triangles such as isosceles triangle, scalene triangle, equilateral triangle and right angled triangle.
Sine rule states that for a triangle with angles A,B and C and corresponding opposite sides a, b, and c, the following formula holds:
[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]
Let the starting point be A, hence the side opposite to the angle = a = distance travelled in north east direction.
Let the point of 60° of northeast be B = 90° + (90° - 60°) = 120°, hence the side opposite to the angle = b = resultant displacement = 8 km.
Let C be the endpoint, hence the side opposite to the angle = c = distance travelled north = 5 km
Using sine rule:
[tex]\frac{b}{sin(B)}=\frac{c}{sin(C)} \\\\\frac{8}{sin(120)}=\frac{5}{sin(C)} \\\\sin(C)=\frac{5*sin(120)}{8} =0.5412\\\\C=sin^{-1}(0.5412)=32.8^o\\\\[/tex]
∠A + ∠B + ∠C = 180° (sum of angle in a triangle)
∠A + 120 + 32.8 = 180
∠A = 27.2°
[tex]\frac{b}{sin(B)}=\frac{a}{sin(A)} \\\\\frac{8}{sin(120)}=\frac{a}{sin(27.2)} \\\\a=\frac{8*sin(27.2)}{sin(120)} \\\\a=4.2\ km[/tex]
Therefore she travelled 4.2 km in the north east direction
