The question is find the height of the tree, given that at two points 65 feet apart on the same side of the tree and in line with it, the angles of elevaton of the top of the tree are 21° 19' and 16°20'.
1) Convert the angles to decimal form:
19' * 1°/60' = 0.32° => 21° 19' = 21.32°
20' * 1°/60' = 0.33° => 16° 20' = 16.33°
2) Deduce the trigonometric ratios from the verbal information.
You can form a triangle with
- horizontal leg x + 65 feet
- elevation angle 16.33°
- vertical leg height of the tree, h
=> trigonometric ratio: tan (16.33) = h /( x + 65) => h = (x+65) * tan(16.33)
You can form a second triangle with:
- horizontal leg x
- elevation angle 21.32°
- vertical leg height of the tree, h
=> trigonometric ratio: tan(21.32) = h / x => h = x * tan(21.32)
Now equal the two expressions for h:
(x+65)*tan(16.33) = x*tan(21.32)
=> x*tan(16.33) + 65*tan(16.33) = x*tan(21.32)
=> x*tan(21.32) - x*tan(16.33) = 65*tan(16.33)
=> x = 65*tan(16.33) / [ tan(21.32) - tan(16.33) ] = 195.73 feet
=> h = 195.73 * tan(21.32) = 76.39 feet.
Answer: 76.39 feet
Answer:
See below
Step-by-step explanation:
If x=1, then 1-1=0, which implies a vertical asymptote at x=1 since dividing by 0 is undefined.
Answer: the slope is 1
Step-by-step explanation:
Slope is basically rise over run. Looking at the graph you see it rises one unit and then goes over to the left by one unit. 1÷1 equals 1 so That is your slope.
Answer:
Step-by-step explanation:
Answer:
6 < x ≤ 20
Step-by-step explanation:
First, let's use the points (0, 50) and (20, 0) to find the equation of the line.
m = Δy / Δx
m = (0 − 50) / (20 − 0)
m = -2.5
y = -2.5x + 50
Now find the time when y = 35.
35 = -2.5x + 50
-15 = -2.5x
x = 6
So there is less than 35 gallons in the barrel when 6 < x ≤ 20.
