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:
I am not sure but I would say rectangular prisim
Step-by-step explanation:
Answer:
x= 3/5
Step-by-step explanation:
Standard form:
5,098,000
Scientific notation.
1) only 1 digit should be before the decimal point.
5.098000
2) only non-zero number must be part of the coefficient. the rest are included in the base of 10.
5.098 x 10^6 Choice D.
Exponent is the number of times the decimal moved from its original placement to its place after the 1st digit.
To find the vertex of the parabola, we need to write it in a vertex form.
y=x² - 8x +12
1) complete the square
y=
x² - 8x +12
y =
x² -2*4x + 4² - 4² +12
y=
(x-4)² -16 +12
2) calculate and write a vertex
y=
(x-4)² -16 +12
y=
(x-4)² - 4
(x-4) ----- x- coordinate of the vertex x=4
y=(x-4)²
- 4 -------y- coordinate of the vertex y = - 4 Vertex is (4, -4).
Answer is (4, -4). No correct answer is given in choices.
