From a point A, due south of a tower , the angle of elevation of the top is 45degree, another point B is due east of the tower and the bearing of B from A is 30degree. Find the angle of elevation of the top of the tower
To find the angle of elevation of the top of the tower, we need to visualize the situation and use some trigonometry.
Here's how to approach the problem:
Step 1: Draw a diagram
Draw a diagram with point A south of the tower and point B east of the tower. Label the angle of elevation at point A as 45 degrees and the bearing of B from A as 30 degrees.
```
A
\
\
\
\ 45°
\
\
Tower \
------------------------------------------------
```
Step 2: Understand the situation
From the information given, we know that A is due south of the tower, and the angle of elevation from A to the top of the tower is 45 degrees. We also know that B is due east of the tower, and the bearing from A to B is 30 degrees.
Step 3: Determine the angle of elevation
To find the angle of elevation at point B, we need to find the angle formed between the line connecting A and B and the horizontal line.
Since the bearing from A to B is 30 degrees, we can subtract this angle from 90 degrees (because the angle between the horizontal line and the line connecting A and B is complementary to the bearing angle). Therefore, the angle between the line connecting A and B and the horizontal line is 90 - 30 = 60 degrees.
Step 4: Apply trigonometry
Now, we have a right-angled triangle formed by the line connecting A and B, the line connecting A and the top of the tower, and the vertical line from the top of the tower.
From the diagram, we can see that the angle of elevation we need to find is the complementary angle to the 60 degrees angle. Therefore, the angle of elevation is 90 - 60 = 30 degrees.
So, the angle of elevation of the top of the tower is 30 degrees.