# Thread: Answer key wrong? Simple trig problem (two right triangles)

1. ## Answer key wrong? Simple trig problem (two right triangles)

There are a lot of discrepancies in the answer key and so I had wanted to verify with another eye if I am correct on this or not.

The question simply relates to a pipe going down the side of a cliff with two bends in it, the second steeper than the first.

i.e..
From flat ground, pipe bends 17 degrees (angle of depression) and is 6.4m long.
Pipe bends down again (37 deg "from horizontal" it says) and is 5.2m long.
How far down has the pipe gone vertically to the nearest metre?

I saw what worked and went with it. Two right triangles at each level, and a cosine (have hypotenuses, adjacent will = height, so use cosine)
Code:
cos(17) = 0.9563, ..., 6.4*0.9563 = 6m
cos(37) = 0.7986, ..., 5.2*0.7986 = 4m
6m + 4m = 10m, however the answer key says 5 metres. There are many flaws in the answer key (them not rounding as instructed in the worksheet giving varying answers) however this one seemed a lot different than a simple rounding issue. Do you see anything wrong with either?

Alexei.

2. ## Re: Answer key wrong? Simple trig problem (two right triangles)

Originally Posted by alexei
There are a lot of discrepancies in the answer key and so I had wanted to verify with another eye if I am correct on this or not.

The question simply relates to a pipe going down the side of a cliff with two bends in it, the second steeper than the first.

i.e..
From flat ground, pipe bends 17 degrees (angle of depression) and is 6.4m long.
Pipe bends down again (37 deg "from horizontal" it says) and is 5.2m long.
How far down has the pipe gone vertically to the nearest metre?

I saw what worked and went with it. Two right triangles at each level, and a cosine (have hypotenuses, adjacent will = height, so use cosine)
Code:
cos(17) = 0.9563, ..., 6.4*0.9563 = 6m
cos(37) = 0.7986, ..., 5.2*0.7986 = 4m
6m + 4m = 10m, however the answer key says 5 metres. There are many flaws in the answer key (them not rounding as instructed in the worksheet giving varying answers) however this one seemed a lot different than a simple rounding issue. Do you see anything wrong with either?

Alexei.
the answer key is correct.

vertical distance = 6.4sin(17) + 5.2sin(37)

3. ## Re: Answer key wrong? Simple trig problem (two right triangles)

Originally Posted by skeeter
the answer key is correct.

vertical distance = 6.4sin(17) + 5.2sin(37)
Why is this so? In reference to the angles of depression, the sine ratio would be finding the horizontal (opposite side) and not the height (adjacent side).

The two adjacent sides added together just make sense to me, as they would be the equivalent of this:

Edit: Looking at it, if the triangles were inverted (on top) sine would reference the vertical sides.. Why would that correct the situation? Picturing the triangle inverted, the opposite would be the adjacent in my image, I do not get why having them under does not work here with cosine. I even recall being shown to do it as I have above and was marked correctly.

5. ## Re: Answer key wrong? Simple trig problem (two right triangles)

Originally Posted by alexei
Why is this so? In reference to the angles of depression, the sine ratio would be finding the horizontal (opposite side) and not the height (adjacent side).

The two adjacent sides added together just make sense to me, as they would be the equivalent of this:

Edit: Looking at it, if the triangles were inverted (on top) sine would reference the vertical sides.. Why would that correct the situation? Picturing the triangle inverted, the opposite would be the adjacent in my image, I do not get why having them under does not work here with cosine. I even recall being shown to do it as I have above and was marked correctly.
...

6. ## Re: Answer key wrong? Simple trig problem (two right triangles)

Hi alexei,
The cosine function defines horizontal distances.Put the angles in the proper place in each of your triangles shown under the canopy.