Right triangles, word problem.

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TwoRocks

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Donna measured the angle of elevation of a church steeple and found it to be 10°. Then she walked 100m towards the steeple and measured the angle of elevation again; this time it was 20°. Find the height of the steeple, assuming that the ground is level.



Here is an image to help you better understand the question. What I have figured out is in red (figured it out using tan(10)=x/100).
I'm not sure where to go from here. How do I use this information to figure out the height?
Please help; this is due in a day and a half.
 
You can set up two equations and solve for x and y.

Let x=the height of the building and y=the distance from where she moved to to the building.

The height of the building, x, from the closer point is x=ytan(20)

Then you get:

\(\displaystyle ytan(20)=(100+y)tan(10)\)

Solve for y and x will fall into place.
 
One approach would be to label the segment from the base of the building to the spot where she stopped walking (100 m from the starting point) y. That gives you two right triangles. One triangle has legs of x and 100 with an angle of 10° and the other triangle has legs of 100+y and x with an angle of 20°. Now you have two equations in two unknowns.
 
Donna measured the angle of elevation of a church steeple and found it to be 10°. Then she walked 100m towards the steeple and measured the angle of elevation again; this time it was 20°. Find the height of the steeple, assuming that the ground is level.

The first observation is made at an angle of elevation of 10º.

The second at an angle of 20º.

The triangle formed by the two observation points and the top of the steeple has angles of 10º, 160º and 10º.

With the distance between the two observation points being 100m, the distance from the second observation point to the steeple top is also 100m.

Therefore, the steeple height is simply 100sin20 = 34.2m.

Just a thought.
 
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