Trig Prob: Given angles of depression, what is the width of the lake? (meters)

[ds197]

Hi,

I don't quite understand this trig problem...

A surveyor in an airplane observes the angle of depression to 2 points (A and B) on the opposite shores of the lake 32° and 45°. What is the width of the lake? (meters)

I started by drawing out the image of what it looks like:

Then the first thing I thought was use the sine law
but I don't have the other length (between the plane and point B) just the side A (9750m)

do I have to find the angles first? Then the length?

Help!

 

[Deleted member 4993]

Hi,

I don't quite understand this trig problem...

A surveyor in an airplane observes the angle of depression to 2 points (A and B) on the opposite shores of the lake 32° and 45°. What is the width of the lake? (meters)

I started by drawing out the image of what it looks like:

Then the first thing I thought was use the sine law
but I don't have the other length (between the plane and point B) just the side A (9750m)

do I have to find the angles first? Then the length?

Help!

In your problem statement there is no reference to the number 9750 m shown in the figure!

What does that (9750 m) refer to?

 

[Quaid]

Hi,

A surveyor in an airplane observes the angle of depression to 2 points (A and B) on the opposite shores of the lake 32° and 45°. What is the width of the lake? (meters)

I started by drawing out the image of what it looks like

Please confirm that the exercise gives 9750m as the distance from the plane to point A, as you have labeled.

Then the first thing I thought was use the sine law but I don't have the other length (between the plane and point B)

just the side A (9750m)

Looking at your diagram, the side measuring 9750 is side b (the side opposite angle B), yes?

In general, the symbols for triangle sides are a,b,c (lower-case), and the symbols for the angles opposite those sides are A,B,C (upper-case), respectively.

The angle at the plane is C; the width of the lake is c (the lake is one of two places that you labeled x; that's confusing).

The Law of Sines will work, I think, and, yes, you need to determine angles B and C, first.

You know the side opposite angle B, and you have enough information to calculate angles B and C.

9750/sin(B) = c/sin(C)

Solve for c.

Cheers

 

[HallsofIvy]

Frankly, the distance from the plane to point A would be a very strange thing to give. I can see no way the surveyor, in the plane, could know that. On the other hand, the altitude of the plane, the length of a perpendicular from the plane to the line through A and B, could be read off the plane's altimeter. Are you sure that the "9750" is not the altitude of the plane?

 

[MissLivia97]

Trig Problem

Hi, I'm stuck on the same problem as well, except the problem is worded a little differently.
In my problem it states, " From an airplane, a surveyor observes two points on the opposite shores of a lake, as shown. How far is it across the lake?
And proceeds to show me this diagram.
Since there is only one side given, and the angles are on the same side, I feel like I can't use both of the angles given to use the Law of Sines, or to calculate all angles in the triangle.
So, my question is, how do I use the two angles given to figure out my answer?

 

[mmm4444bot]

Hi, I'm stuck on the same problem as well, except the problem is worded a little differently.

… Since there is only one side given, and the angles are on the same side, I feel like I can't use both of the angles given to use the Law of Sines, or to calculate all angles in the triangle.

It's the same exercise. Did you read post #3, in this thread? It explains how to solve the exercise.

On your diagram, label the vertex at the airplane as point C.

Now you have triangle ABC, and standard notation says that side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C. You've been asked to find the length of side c.

The length of side b is given.

You can determine angle C, from the two given angles, yes? (Think difference.)

You can determine angle B because it's one of a pair of alternate interior angles (one of which is given).



Using angles B and C, along with sides b and c, in the Law of Sines will give you an equation to solve for c.

If you get stuck, please show us your work. :cool: