A rocket flies 150 km on a bearing of 042 degrees. It then flies 45 km on a bearing of 165 degrees. Find

a. The bearing
b. The distance of the rocket from the starting point?

(a) convert to x-y, add the components, then find the bearing by arctan of displaceement

(b) The distance z is found via
z^2 = 150^2 + 45^2 - 2*150*45*cos57°

To find the bearing and the distance of the rocket from the starting point, we can use trigonometry and vector addition.

Let's break down the problem step by step:

Step 1: Convert the bearing angles to compass headings.
- The bearing of 042 degrees is equivalent to the compass heading of North 42 degrees East.
- The bearing of 165 degrees is equivalent to the compass heading of South 75 degrees East.

Step 2: Convert the compass headings to Cartesian coordinates.
- North 42 degrees East can be represented as (cos(42), sin(42)). Let's call this vector A.
- South 75 degrees East can be represented as (cos(75), -sin(75)). Let's call this vector B.

Step 3: Find the resultant vector by adding the two vectors.
- To find the resultant vector, add vector A and vector B:
R = A + B = (cos(42) + cos(75), sin(42) - sin(75))

Step 4: Find the magnitude and direction of the resultant vector.
- The magnitude of the resultant vector can be found using the Pythagorean theorem:
Magnitude = √((cos(42) + cos(75))^2 + (sin(42) - sin(75))^2)

- The direction or bearing of the resultant vector can be found using the inverse tangent:
Bearing = arctan((sin(42) - sin(75)) / (cos(42) + cos(75)))

Step 5: Find the distance of the rocket from the starting point.
- The distance can be found simply by summing the distances covered:
Distance = 150 km + 45 km = 195 km

So, to summarize:
a. The bearing of the rocket is the bearing of the resultant vector calculated in Step 4.
b. The distance of the rocket from the starting point is 195 km.

To find the exact values of the bearing and distance, you can use a scientific calculator or programming language that supports trigonometric functions.