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

[bnd_20191]

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.

 

[haruspex]

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.

 

[neilparker62]

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.

 

[jbriggs444]

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.

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.

 

[bnd_20191]

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.

 

[jbriggs444]

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