Xavier is installing two sections of pipe. The first section is 4.1 m long and makes an angle of 18 below the horizontal. The second section of pipe is attached at the end of the first, with a bend. The second pipe is 5.3 m long and makes an angle of 29 below the horizontal. What is the total drop from the start of the first pipe to the end of the second pipe?
a. 3.8 m
c. 2.7 m
b. 5.2 m
d. 2.5 m
We can split the problem into two parts: the drop caused by the first section of pipe, and the drop caused by the second section of pipe.
For the first section of pipe, we can use the given length of 4.1 m and angle of 18 below the horizontal. We can use trigonometry to find the vertical component of this drop.
The vertical component of the drop caused by the first section of pipe is given by:
Vertical drop = length of pipe * sine(angle)
Vertical drop = 4.1 m * sin(18°)
Vertical drop ≈ 1.39 m
For the second section of pipe, we can use the given length of 5.3 m and angle of 29 below the horizontal. Again, we can use trigonometry to find the vertical component of this drop.
The vertical component of the drop caused by the second section of pipe is given by:
Vertical drop = length of pipe * sine(angle)
Vertical drop = 5.3 m * sin(29°)
Vertical drop ≈ 2.55 m
Now, to find the total drop, we can sum the drops caused by each section of pipe:
Total drop = drop caused by first section + drop caused by second section
Total drop ≈ 1.39 m + 2.55 m
Total drop ≈ 3.94 m
Therefore, the total drop from the start of the first pipe to the end of the second pipe is approximately 3.94 m.
The closest answer choice is a. 3.8 m.