A, B, C are three points on a horizontal plane, where A is due south of B. The bearing of C from A is 060 degrees. At B, there is a vertical mast BD. The angles of elevation of its top D from A and C are 25 degrees and 20 degrees respectively. Find the bearing of B from C.
take a look at the 2nd related question below.
bearing
To find the bearing of B from C, we need to understand the relationship between the angles and the given information.
Let's analyze the scenario step by step:
1. Draw a horizontal plane and plot points A, B, and C. Label A due south of B.
2. Since the bearing of C from A is given as 060 degrees, we can draw a line from point A to C and mark an angle of 60 degrees.
3. Draw a vertical line from point B upward to represent the mast BD.
4. According to the problem, the angle of elevation of D from A is 25 degrees. This means we can draw a line from point A to D, forming a right triangle ABD.
5. Similarly, the angle of elevation of D from C is given as 20 degrees. Thus, we can draw a line from point C to D, forming right triangle CBD.
Now, let's solve for the bearing of B from C:
1. In triangle ABD, we have the angle ADB as 90 degrees (since it's a right triangle), and the angle A to be 25 degrees.
2. Using the given angle of elevation of D from A, we can determine the angle BDA by subtracting the given angle from 90 degrees:
BDA = 90 - 25
= 65 degrees
3. In triangle CBD, we have the angle CDB as 90 degrees (also a right triangle), and the angle C to be 60 degrees.
4. Subtract the given angle of elevation of D from C to determine the angle BDC:
BDC = 90 - 20
= 70 degrees
5. Now, to find the bearing of B from C, we need to calculate the angle BCD. Since it's a triangle, the sum of the angles is 180 degrees. Therefore:
BCD = 180 - (BDC + BDA)
= 180 - (70 + 65)
= 180 - 135
= 45 degrees
Thus, the bearing of B from C is 045 degrees.