trigonometry prob. . any help appreciated, I'm not sure what angle i am looking for exactly?

Question

from a window 30 metres above the street the angle of elevation to the top of the building across the street is 50 degrees and the angle of depression to the base of this building is 20 degrees. Find the height of the building across the street.

Answer 1

You need two right triangles, I've attached a diagram...
http://img247.imageshack.us/img247/7576/bldgny3.gif

The bottom triangle has an angle of depression of 20°. We know the opposite side is 30m (same height as the window, assuming a level street). We want to figure the adjacent side 'A', being the distance across the street.

From the SOH-CAH-TOA mnemonic --> Tan(angle) = Opposite/Adjacent.

So tan(20°) = 30/A

Solving for A:
A = 30/tan(20°)
A ≈ 82.4m

Now we look at the top triangle. The angle of elevation is 50°. We now know the adjacent side is 82.4m. We need to determine the opposite side 'O'.

Again, tan(50°) = O/82.4

Solving for O:
O = tan(50°) * 82.4
O ≈ 98.2m

The total height of the building is the sum of the two heights (30m to the window and 98.2m to the roof).

So the building is approximately 128.2m tall.

Answer 2

Since the angle of depression is 20 degrees, the distance between the buildings must be 30/tan(20).

Since the angle of elevation to the top of the other building is 50 degrees, then the distance from 30 feet above street level to the top of the building must be d =(30 tan50)/tan20
Therefore total height is 30 + (30 tan50)/tan20 which is exact.

tan 50 = 1.1918 and tan 20 = .3640, so an approximate answer is
height = 30+30(1.1918)/.364 = 30+98.2= 128.2 meters

Answer 3

Draw a diagram. In the bottom triangle, base is d, distance between the buildings, height is 30, and angle opposite 30 is 20°. So 30/d = tan 20°, d = 30/tan 20.

In the top triangle, base is d, height is h, and angle opposite h is 50°. So h/d = tan 50.

Now substitute 30/tan 20 for d in the second equation. You get
h/(30/tan 20) = tan 50
h = (30 tan 50)/tan 20 = 98.23 m.

Since h is the part of the building ABOVE the window, add another 30 m. The height of the building is 128.23 m.

d = 30/tan 20 = 82.42 m for the distance between buildings.

Answer 4

I'm not sure I understand what you mean by "depression to the base", but here's my best guess.

30 m above ground you stand and measure 50 (from the horizontal) to the top of the building across the street.

You then measure 20 (from the horizontal) downward to the base of the building.

Yes?

You have two triangles. One has a leg that is 30 m, and angle that is 20 deg. Find the horizontal leg.

x = 30tan(20) = 10.92 m

Use this to find the height of the upper triangle that has angle 50 degrees and base 10.92 m

y = 10.92tan(50) = 13.0 m

the height f the building will be the sum of the heights of the two triangles.....30m...and 13 m, so the height of the building is 43 m.

Incidentally, you are 10.92 m from that building.

This is valid IF I understood your question correctly and my assumption was correct.

Answer 5

Draw the figure and draw a horizontal line across from the window to the other building. This hits the other building at a hieght of 30 m. You need the remaining part of the other building.

You can calculate the distance between the buildings d by using tan 20 = 30/d

Then use that to calculate the missing part of the building b:
tan 50 = b/d

Then add it to 30

Answer 6

So the windows is 30 meters high, and the angle from base of the other bldg to the top is 70 degrees. The angle at the bottom is 70 degrees and the top is 40 degrees. SO you have two triangles
20-90-70 (degrees) with one side being 30 meters
50-90-40 with no sides yet, but if you solve the first trianlge you'll get one side of this one.

Answer 7

let the height of the building be H
let the horizontal distance be x
the equations are
H-30/x=tan50*
30/x=tan20*
H=xtan50+30
x=30cot20
=>30tan70
so H=30tan70tan50+30
please plug in the values and simplify
ido not use a calculator