In the afternoon, the person (who is 1.8 m tall) casts a shadow that is 10 m. The distance along the ground from the person (H) to the tree (G) is 24 m, and the distance from the tree (G) to the building (F) is 150 m. Calculate the height of the tree and the building. Round answers to the nearest tenth of a meter and show all your work.
Answers
Answer:
The height of the tree is 6.12 meters and the height of the building is 33.12 meters.
Step-by-step explanation:
Since the person is 1.8 meters tall, HC = 1.8
And since their shadow is 10 meters long, HD = 10.
We are also given that GH is 24 meters and that FG is 150 meters.
Height of the Tree:
The height of the tree is given by GB.
Again, since m∠BGD = m∠CHD = 90°, ∠BGD ≅ ∠CHD.
Likewise, ∠D ≅ ∠D. So, by AA-Similarity:
[tex]\displaystyle \Delta BGD\sim \Delta CHD[/tex]
Corresponding parts of similar triangles are in proportion. Therefore:
[tex]\displaystyle \frac{GB}{GD}=\frac{HC}{HD}[/tex]
Note that:
[tex]GD=GH+HD[/tex]
Find GD:
[tex]GD=(24)+(10)=34[/tex]
Substitute the known values into the proportion:
[tex]\displaystyle \frac{GB}{34}=\frac{1.8}{10}[/tex]
Cross-multiply:
[tex]10GB=61.2[/tex]
Therefore:
[tex]GB=6.12\text{ meters}[/tex]
The height of the tree is 6.12 meters.
Height of the Building:
The height of the building is given by FA.
Since m∠AFD = m∠CHD = 90°, ∠AFD ≅ ∠CHD.
∠D ≅ ∠D. So, by AA-Similarity:
[tex]\Delta AFD\sim \Delta CHD[/tex]
Corresponding parts of similar triangles are in proportion. Therefore:
[tex]\displaystyle \frac{FA}{FD}=\frac{HC}{HD}[/tex]
Note that:
[tex]FD=FG+GH+HD[/tex]
Find FD:
[tex]FD=(150)+(24)+(10)=184[/tex]
Substitute the known values into the proportion:
[tex]\displaystyle \frac{FA}{184}=\frac{1.8}{10}[/tex]
Cross-multiply:
[tex]10FA=331.2[/tex]
Therefore:
[tex]FA=33.12\text{ meters}[/tex]
The height of the building is 33.12 meters.
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use the diagram to find the value of x
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explanation: i forgot exactly the name of the rule but since the angle 12 is in the same place as x is with the parallel lines, angle 12 and angle x share the same measurements so angle x=12
Answer:
4
Step-by-step explanation:
18x = 12(x+2)
18x = 12x+24
18x-12x = 24
6x = 24
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Jackie played the first 8 minutes of a basketball game. Layla then replaced
her for the rest of the half. Layla started the second half and was replaced by
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A. The number of players who played during the game
B. The number of minutes Layla played in the second half
C. The total number of minutes Jackie played
D. The length of the half
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Answer:
Step-by-step explanation:
d
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Answer:
B. 7x - 5
Step-by-step explanation:
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Answer:
its 30 or 24
Step-by-step explanation:
but its most likely 30
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9514 1404 393
Answer:
see attached
Step-by-step explanation:
It is easier to construct the center using a compass and straightedge (and pencil). The center is where the medians meet. A median is drawn from a vertex to the midpoint of the opposite side.
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With a compass and straightedge, the usual process of constructing the bisector of a line segment is used.
Rearrange the formula to make x the subject.
y = x -5
Answers
Answer:
[tex]x=y+5[/tex]
Step-by-step explanation:
[tex]y=x-5[/tex]
[tex]y+5=x[/tex]
[tex]x=y+5[/tex]
Si: Tg θ =√2 ∧ θ es agudo √7 Calcular: A = 3(Sen θ + Cos θ) - √7
Answers
Answer:
[tex]A \approx 1.488[/tex]
Step-by-step explanation:
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[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex] (2)
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (3)
Si [tex]\theta[/tex] es agudo, entonces [tex]x, y > 0[/tex].
De (1), suponemos [tex]x = 1[/tex] que [tex]y = \sqrt{2}[/tex], entonces los valores de las funciones seno y coseno:
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[tex]A \approx 1.488[/tex]
Hehehejdjkskjsknssnnsnajsbsb
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Step-by-step explanation:
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Answers
Answer:
25, 24, 7
Step-by-step explanation:
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B) 0
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Answer:
D
Step-by-step explanation:
Lsh=rhs
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Answers
Answer:
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Step-by-step explanation:
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Which system of equations has infinitely many solutions?
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Answer:
what do you need help with?
Step-by-step explanation:
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Answers
Answer:
m=4 and c=-1
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
Step-by-step explanation:
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Answer:
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Answers
Answer:
Step-by-step explanation:
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Answers
Answer:
AB
Step-by-step explanation:
The diameter has to pass through the center of the circle and tough the outside of the circle on both ends
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ED and BA
Answer:
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Answers
Answer:
$750
Step-by-step explanation:
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ASAP BRAINLIEST IF RIGHT 30 POINTS NO NEED FOR WORK
At a restaurant, diners earn 1 point for every $2 they spend, plus 25 bonus points on their first meal. Function f represents the number of points earned as a function of the total amount spent x. Which function represents the total amount spent as a function of the number of points earned?
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D. f−1(x) = 0.5x + 50
Answers
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Answers
Answer:
[tex](m−15)(m+2)[/tex]
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[tex] m² - 13m - 30?[/tex]
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[tex] {x}^{2} +bx+c[/tex]
[tex](m−15)(m+2)[/tex]
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Answers
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Step-by-step explanation:
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Answers
Answer:
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Answers
Answer:
70kg can be purchased for Rs 525
Step-by-step explanation:
Let the quantity of rice that can be bought with Rs 525 be = x
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Answers
Answer:
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Answers
Answer:
the answer is the second option
Step-by-step explanation:
it is
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Answers
Answer:
7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
4 1/5 ÷ 3/5
Change to improper fractions
4 1/5 = ( 5*4+1) /5 = 21/5
21/5 ÷ 3/5
Copy dot flip
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21/ * 5/5
7 * 1
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Answers
2. 3, 1 and then 2
3.a
4. b
I'll give brainliest!
Answers
Step-by-step explanation:
Answer:
D. 4 And 8
#Carryonlearning
Answer:
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Step-by-step explanation:
Find the area and the perimeter of this square
2√3x
Answers
The perimeter of a square is equal to 4 times the side length.
=4
P
=
4
s
where
P
is the perimeter and
s
is the side length of the square.
If the side length of the square is 3−2
3
x
−
2
units, then let =3−2
s
=
3
x
−
2
The perimeter would be:
=4(3−2)
P
=
4
(
3
x
−
2
)
=4(3)−4(2)
P
=
4
(
3
x
)
−
4
(
2
)
=12−8
P
=
12
x
−
8
Therefore the perimeter of the square is: 12−8
12
x
−
8
units.
Regards,
. ℎ
A
a
r
o
n
M
.
C
h
a
o
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Profile photo for Arturo Ordonez-Hernandez
Arturo Ordonez-Hernandez, Associate Programmer/Analyst at Weber State University (2018-present)
Answered March 8
A square is an equilateral rectangle.
So, we know that, for a rectangle,
=2+2
P
=
2
l
+
2
w
For a square,
=
l
=
w
so,
=4=4
P
=
4
l
=
4
w
Therefore,
=4(3−2)
P
=
4
(
3
x
−
2
)
=12−4
P
=
12
x
−
4
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Profile photo for Len Fyfe
Len Fyfe, B.Ed. Mathematics & Physics, Chemistry, Maths, and Computer Science, Lakehead University (2005)
Answered March 4
side length is 3x-2
each of the four sides is the same length
P = 4(3x-2) factored form
P = 12x - 8 expanded form
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