I don't understand how to setup this problem?

mrjust

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Dec 12, 2012
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I'm having trouble setting up the triangle based on the info given:

A boat is at point A some meters away from a vertical rock cliff. The angle of elevation from the boat to the top of the cliff is 28 degrees. The boat then sails 50 meters towards the base of the cliff and stops at point B. From point B the angle of elevation to the top of the cliff is 70 degrees.
a.) Sketch and label the figure illustrating the situation.
b.) How tall is the cliff?

Thanks in advanced for your help.
 
What kind of help do you want?

Do you sufficiently understand the given info to draw the picture?

There are two right triangles. Have you learned any right-triangle trig? You posted on the algebra board.

One triangle has angle 28 degrees, with opposite side h (for height) and adjacent side A.

The other has angle 70 degrees, with opposite side h and adjacent side A-50.

Can you write the sine of each angle? The sine of each angle equals the corresponding ratio "opposite/adjacent". Do you know what this ratio means?

Writing sin(degrees)=opposite/adjacent gives two equations (in terms of A and h), each of which can each be solved for h.

Equate the results for h, and you get a single equation containing A.

Solve for A.

Once you have the value for A, you can use it to find h.

I'm not sure whether this info helps you. Do you have any specific questions? Can you show any work?
 
I needed to be shown step-by-step, because I don't understand the proper way to set up the angles and points.
What confused me is the location of part A and B.
I did draw two triangles:

Untitled.jpg
I do have an understanding of Trigonometry, and sorry for posting in the wrong forum.
Based on the triangles I drew I solved for A:

(50/sine42)=(a/sine28)
a= approximately 35 meters

Then using a I solve for h:

(h/sine70)=(35/sin90)
h= approximately 32.89 meters

Not sure if this is right?

Based on your information I don't see how I have 2 right triangles? Would you be able to draw out the triangle and attach it, I need a visual examples? Thank you very much.
 
Call the point at the base of the cliff "C" and the point at the top of the cliff "D". One right triangle is BCD and the other is ACD.
 
I needed to be shown step-by-step, because I don't understand the proper way to set up the angles and points.
What confused me is the location of part A and B.
I did draw two triangles:

View attachment 2513
I do have an understanding of Trigonometry, and sorry for posting in the wrong forum.
Based on the triangles I drew I solved for A:

(50/sine42)=(a/sine28)
a= approximately 35 meters

Then using a I solve for h:

(h/sine70)=(35/sin90)
h= approximately 32.89 meters

Not sure if this is right?

Based on your information I don't see how I have 2 right triangles? Would you be able to draw out the triangle and attach it, I need a visual examples? Thank you very much.

Your picture is correct.

Now

Let BC = x and CD = h

Then,

From triangle ACD

tan(28°) = CD/CA = h/(x+50) ............................................(1)

and From triangle BCD

tan(70°) = CD/CB = h/(x)...................................................(2)

Then dividing (2) by (1), we get:

tan(70°)/tan(28°) = (x+50)/x ............................................(3)

Now solve (3) to calculate 'x'

Then use this value of 'x' in (2) [or (1)] - to get 'h'
 
Using Scaling

I needed to be shown step-by-step, because I don't understand the proper way to set up the angles and points.
What confused me is the location of part A and B.
I did draw two triangles:

View attachment 2513
I do have an understanding of Trigonometry, and sorry for posting in the wrong forum.
Based on the triangles I drew I solved for A:

(50/sine42)=(a/sine28)
a= approximately 35 meters

Then using a I solve for h:

(h/sine70)=(35/sin90)
h= approximately 32.89 meters

Not sure if this is right?

Based on your information I don't see how I have 2 right triangles? Would you be able to draw out the triangle and attach it, I need a visual examples? Thank you very much.

Here is a scaled down model that is rotated.
All angles have been unchanged (definition of scaling)
h=1 and is now the base.

Untitled.jpg
The tangent of the relevant angles is used to get the location of A and B given that h=1.

SOLUTION:
We find that A-B needs to be scaled from 1.52 to 50.
A scale factor of 32.89 will do that.
Therefore, h=1 will scale up to h=32.89
 
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