4. A,B and C are points on a horizontal plane.
A is 75 m from C on a bearing of 210 degrees and the bearing of B from C is 120 degrees. The bearing of B from A is 075 degrees.
From A the angle of elevation of the top T of a vertical towel at C is 42 degrees.
Find
a. the distance BC
b.The height of the tower
c. the angle of elevation
If possible could you please draw the diagram- a sketch is fine.
And provide the working out please.
Thanks
To solve this problem, let's break it down step by step.
Step 1: Draw the diagram (the diagram is not visible in this text-based format, but I will describe it to you to follow along):
- Draw three points A, B, and C on a horizontal plane.
- A is 75 m away from C and on a bearing of 210 degrees (direction clockwise from the north).
- The bearing of B from C is 120 degrees.
- The bearing of B from A is 075 degrees.
- The top of the vertical towel is labeled as T.
Step 2: Find the distance BC.
We can use the Sine Rule to find the distance BC.
First, we need to find the angle at point A. Since the bearing of B from A is 075 degrees, we subtract it from 180 degrees to obtain an angle of 105 degrees at point A.
Using the Sine Rule, we can write:
BCsin(A) = ACsin(B)
BCsin(105) = 75sin(120)
BC = (75sin(120))/sin(105)
Using a calculator, you can compute this value to find the distance BC.
Step 3: Find the height of the tower.
From point A, the angle of elevation of the top T of the tower is given as 42 degrees.
We can use the tangent function to find the height of the tower. Tangent is defined as the opposite side divided by the adjacent side.
tangent(42) = height of the tower / BC
height of the tower = BC * tangent(42)
Again, using a calculator, you can compute the value of the height of the tower.
Step 4: Find the angle of elevation.
To find the angle of elevation, we need to use the inverse tangent function.
angle of elevation = inverse tangent(height of the tower / AC)
Using a calculator, find the inverse tangent of the height of the tower divided by the distance AC to obtain the angle of elevation.
With these steps, you should be able to find the answers to the questions:
a. The distance BC
b. The height of the tower
c. The angle of elevation