Question

A boy walks 40m from a city X on a bearing of 040° to a city Y. She then walks 40m on a bearing of 140° to a city Z. Find the bearing of Z from city X.

a) 35°
b) 50°
c)90°

Answer 1

Answer: option C.

Explanation:

If city X is in the point (0,0)

Now, we can use that a displacement of L in distance with an angle A, gives us that the components of the displacement are:

X = L*cos(A)

Y = L*sin(A)

So we know that the city Y is located in:

(40m*cos(40°), 40m*sin(40°))

Now, from this point he moves other 40m with an angle of 140°.

The new position is

(40m*cos(40°) + 40m*cos(140°), 40m*sin(40°) + 40m*sin(140°))

this is:

40m*(cos(40°) + cos(140°), sin(40°) + sin(140°)) = 40m*( 0, 1.28)

the new position is (0, 51.2m)

This means that for a new displacement L and angle A we have:

X = L*cos(A) = 0

Y = L*sin(A) = 51.2m

Cos(A) is only 0 when A = 90° or 270°,

and we know that sin(90°) = 1 and sin(270°) = -1

As we have a positive number in the Y equation, we can conclude that A must be 90°.

Then

Y = L*sin(90°) = L = 51.2m

Here we finded that the bearing of Z from city X is 90°