Angle of Depression Help: Using the Sine Rule to Solve for Unknown Angles

In summary, the conversation was about using the sine rule to figure out a problem involving angles and slopes. The individual tried to use the angle of depression and the slope of the path to determine the angle, but it did not seem to be correct. They also mentioned a diagram with a road, a path, and water, but were unable to understand it from the given words. The conversation ended with suggesting a different drawing to better understand the problem.
  • #1
bnd_20191
6
0
Homework Statement
James' eye are 150cm above the ground. When he was standing on the path, the edge of the road was at an angle of depression of 10 degrees. After walking down the 5 degree slope of the path, 10m towards the water, the angle of depression increased to 17 degrees. How much further would he need to walk to reach the road.
Relevant Equations
Angle of Elevation and Depression
Sin, Cosine Rule
Is it like using the sine rule to figure it out:
1.5/sin 68 = x/sin 17 = 0.47 which doesn't seem to be correct. I tried to determine the angle. I though the 5 degree slope means it could be 95 degrees cause the triangle looks like a right angle triangle.
 
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  • #2
Is there a diagram with this? I am unable to figure out the picture from the words. It starts off with just a path and a road (is there a kerb?), then there is mention of water.
 
  • #3
I would guess he's walking down a 5 degree slope towards a road. Water might be further down the slope but is irrelevant since the angles of depression are wrt road.
 
  • #4
neilparker62 said:
I would guess he's walking down a 5 degree slope towards a road.

Guessing, one of PF's time-honored practices.

A problem with the simplest interpretation is that it seems that too much information has been given. However, after working through the problem, it turns out that all of the information is self-consistent under the above interpretation.
bnd_20191 said:
1.5/sin 68
It would be good to provide an explanation on how you arrived at the 68. It appears that you have taken the angle of depression (17 degrees after the downhill stroll) and added it to the slope of the path (given as 5 degrees), subtracted from 90 degrees and taken the sine.

Per Google, the angle of depression is conventionally referenced against the horizontal, not against the local surface.

A drawing to show your thought processes would help enormously.
 
  • #5
bnd_20191 said:
Is it like using the sine rule to figure it out:
1.5/sin 68 = x/sin 17 = 0.47 which doesn't seem to be correct. I tried to determine the angle. I though the 5 degree slope means it could be 95 degrees cause the triangle looks like a right angle triangle.
 

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  • #6
Try this drawing instead. [Clearly I am not an artist]
 

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Related to Angle of Depression Help: Using the Sine Rule to Solve for Unknown Angles

1. What is the sine rule?

The sine rule, also known as the law of sines, is a mathematical rule used to find the missing side lengths or angles in a triangle when given the measurements of other sides and angles. It states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.

2. How do I use the sine rule to solve for unknown angles?

To use the sine rule to solve for unknown angles, you will need to know at least two angle measurements and the length of the side opposite one of those angles. Then, you can use the formula: sin(A)/a = sin(B)/b = sin(C)/c, where A, B, and C are the angles and a, b, and c are the corresponding sides. You can rearrange this formula to solve for the unknown angle by taking the inverse sine of both sides.

3. Can the sine rule be used for all types of triangles?

Yes, the sine rule can be used for all types of triangles, including right triangles, acute triangles, and obtuse triangles. It is a general rule that applies to all triangles, as long as you have enough information about the triangle to use the formula.

4. What is the difference between the sine rule and the cosine rule?

The sine rule and the cosine rule are both used to find the missing sides or angles in a triangle. However, the sine rule is used when you have two angles and the length of the side opposite one of those angles, while the cosine rule is used when you have two sides and the angle between them. The sine rule uses the ratios of the sides and angles, while the cosine rule uses the squares of the sides.

5. Are there any special cases when using the sine rule?

Yes, there are two special cases when using the sine rule. The first is the ambiguous case, which occurs when you have two possible triangles that can be formed with the given information. In this case, you may need to use additional information or the cosine rule to determine which triangle is correct. The second special case is when one of the angles is a right angle (90 degrees), in which case you can use the Pythagorean theorem to solve for the missing side length.

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