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 60-ft 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. 30-60-90 special triangle
draw this out to see that you need to find side a (shorter side) of triangle ABC
30-60-90 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.)
1. To find the height of the building, we can use trigonometry. Let's denote the height of the building as 'h' and the distance of the first point from the base of the building as 'x'.
We have two right-angled triangles here:
Triangle 1: Base = x, Height = h
Angle of elevation = 20 degrees
Triangle 2: Base = x + 25 feet (since the second point is 25 feet farther away), Height = h
Angle of elevation = 12 degrees
In both triangles, we can use the tangent function to relate the angle of elevation to the height and base.
In Triangle 1: tan(20 degrees) = h/x
In Triangle 2: tan(12 degrees) = h/(x + 25)
Now, we can solve these two equations simultaneously to find the values of h and x.
2. In this case, we have the height of the radio antenna, which is 60 feet. We need to find the height of the hill.
Similar to the previous question, we have two right-angled triangles:
Triangle 1: Base = x (distance from the point on the ground to the base of the hill), Height = unknown
Angle of elevation = 39 degrees
Triangle 2: Base = x, Height = 60 ft (height of the radio antenna)
Angle of elevation = 36 degrees
Using the tangent function, we can relate the angles of elevation to the corresponding heights and bases:
In Triangle 1: tan(39 degrees) = unknown/x
In Triangle 2: tan(36 degrees) = 60/x
By solving these two equations simultaneously, we can find the height of the hill.
3. Let's denote the height of the shorter building as 'h' and the height of the taller building as 500 feet. The distance between the two buildings is given as 10 feet.
We have a right-angled triangle with the base being the distance between the buildings (10 feet) and the height being the height difference between the two buildings (500 ft - h).
The angle of elevation from the top of the shorter building to the top of the taller building is given as 30 degrees.
Using the tangent function, we can relate the angle of elevation to the height and base of the triangle:
tan(30 degrees) = (500 ft - h) / 10 ft
By solving this equation, we can find the height of the shorter building.