PreCalculus
posted by Jay on .
1.The angle of elevation to top of a building from a point on the ground 20degrees and the angle of elevation from a point to 25 feet farther away is 12degrees. Find the height of the building.
2.From a point on the ground, the angle of elevation to the top of a 60ft radio antenna sitting atop a hill is 39degrees. The angle of elevation to the top from the same point on the ground is 36 degrees. How high is the hill to the nearest foot?
3.Two different height buildings are 10 feet apart. The angle of elevation from the top of the shorter building to the top of the taller building is 30 degrees. If the taller building is 500 feet tall, how tall is the shorter building?

I think the tutors like you to post each problem as a separate post.

O thanks for the tip. New here. Well and friend helped me figure out 1 and 2 since they were basically the same question. I found out that I had trouble actually doing the algebra once I had the equations. But I'm still a little confused on how to set up number 3.

3. 306090 special triangle
draw this out to see that you need to find side a (shorter side) of triangle ABC
306090 triangle have sides in the ratio of 1 : sqrt 3 : 2 (a : b : c)
Since side b = 10
cos 30 = b/c = 10/c
since ratio of b/c = sqrt 3/2
sqrt 3/2 = 10/c
cross multiply
c * sqrt 3 = 20
c = 20/sqrt 3 = 11.5470
Need to find side a
sin 30 = a/c = a/11.5470
since ratio of a/c = 1/2
1/2 = a/11.5470
a = 5.7735
from picture that you drew you will see
that
500  side a = height of shorter blding
500  5.7735 = 494.2265' 
The angle of elevation from a point on the ground to the top of a post is 15°. The point is 100 meters from the base of the post. To the nearest meter, how tall is the post?

The angle of elevation to the top of a building is 4° from the ground when viewed 2 miles from the building. Estimate the height of the building in feet. (Round your answer to one decimal place.)