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
As I read this one, is just a decay exponential equation... so
A = P(1 + r)ᵗ where "t" is days passed. . hmm in this case is decay, so negative rate A = P(1 - r)ᵗ, and the decimal amount would be 0.00877 for the rate
62% of P, the original value, is just 0.62P, now... if we hmm take P as just 1, it could be any amount, but 62% of 1,000,000 is just 62% of 1 times 1,000,000
so, for the sake of comparing it with a percentage, 1 will do
Use a calculator 5/68 = 5 ÷ 68 = ______
Answer:
Point-slope form: y-4=2(x+1)
Slope intercept form: y=2x+6
I hope this helps!