Law of Sines problem seemingly without enough info.

[gGo]

How is there enough information to solve this problem? The height of the tower isn't given. The horizontal distance of... anything... isn't given. How can this possibly be solved? Chapter is the Law of Sines (but we also have Law of Cosines and other stuff)

 

[khansaheb]

How is there enough information to solve this problem? The height of the tower isn't given. The horizontal distance of... anything... isn't given. How can this possibly be solved? Chapter is the Law of Sines (but we also have Law of Cosines and other stuff)
View attachment 37669

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[Dr.Peterson]

How is there enough information to solve this problem? The height of the tower isn't given. The horizontal distance of... anything... isn't given. How can this possibly be solved? Chapter is the Law of Sines (but we also have Law of Cosines and other stuff)
View attachment 37669

There's enough data to construct a drawing, so there must be enough to calculate all the values:

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You have one side of triangle ACD, and can calculate all of the angles. So you can find the required side, AD.

In other words, the way to answer your question is to draw a picture, label it, and then work out whatever you can; then you'll know more.

 

[gGo]

There's enough data to construct a drawing, so there must be enough to calculate all the values:

View attachment 37671​

You have one side of triangle ACD, and can calculate all of the angles. So you can find the required side, AD.

In other words, the way to answer your question is to draw a picture, label it, and then work out whatever you can; then you'll know more.

TY. I didn't see the drawing that way since the hill didn't have a straight slope. It was confusing.

 

[Dr.Peterson]

TY. I didn't see the drawing that way since the hill didn't have a straight slope. It was confusing.

Yes, the problem is actually bad, if you focus on the picture. It isn't actually true in the drawing that the 150 meter distance ends at the base of the tower; I had to idealize the drawing, using only what was said in words, to make sense of the question. Unfortunately, a lot of math problems are unrealistic that way. You were right if the goal were to solve a real-life problem, for which you'd need a few more measurements:

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The picture doesn't even show the 150 m as being in the same direction as the measured 58 degree angle. I think the picture was made after the problem was written, and was not checked for agreement with the highly idealized problem. I made my drawing from the words, not the picture.