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.
Related Questions
Which expression is a factor of 21x2 + 13x – 20?
Answers
Answer:
B. 7x - 5
Step-by-step explanation:
A sum of money is shared between 2 friends in the ratio 2 : 3. If the larger
share is $450. What is the total sum shared?
Answers
Answer:
$750
Step-by-step explanation:
Larger share = $450
Smaller share : Larger share :: 2 : 3
Smaller share = (larger share x 2) / 3
= (450x2)/3
= 300
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= $450 + $300 = $750
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Answers
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Answer:
4
Step-by-step explanation:
18x = 12(x+2)
18x = 12x+24
18x-12x = 24
6x = 24
x = 4
Using the Pythagorean Theorem, find the distance between the points.
Answers
Answer:
(5,7,8.6)
Step-by-step explanation:
Create a line on each the x axis and the y axis which intersects at a right triangle. The x axis line is 7 squares and the y axis is 5 squares. Now you can use the Pythagorean theorem.
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7^2+5^2=c^2
49+25=c^2
74=c^2
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What is the answer to this division question?
Answers
Answer:
7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
4 1/5 ÷ 3/5
Change to improper fractions
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21/5 ÷ 3/5
Copy dot flip
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Rewriting
21/ * 5/5
7 * 1
7
Which is the graph of y - 3 = -2/3(x + 6)?
Answers
Answer:
Step-by-step explanation:
y - 3 = -2/3(x + 6) Remove the brackets on the right
y - 3 = -2/3x - 2/3 * 6 Simplify the right
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y = - 2/3 x - 1
I'm going to enclose the graph. Pick the one that has a y intercept at (0,-1) and and an x intercept of (-1.5, 0)goes from the lower right to the upper left as the graph below shows.
Need more help again
Answers
Answer:
QSR = 68º
Step-by-step explanation:
TSQ + QSR = TSR
15x + (10x - 2) = 173
Combine like terms
25x = 175
Divide both sides by 25
x = 7
QSR = 10x - 2
QSR = 10(7) - 2
QSR = 68º
CAN SOMEONE HELP ME OUT, PLEASE AND THANK YOU.
Answers
Answer:
what do you need help with?
Step-by-step explanation:
Write an equation in
slope-intercept form that
passes through (-6, -2)
and has a y-intercept
located at y= -5
Answers
Answer:
y = -1/2 x -5
Step-by-step explanation:
The slope intercept form of an equation is
y = mx+b where m is the slope and b is the y intercept
We know b
y = mx-5
Substitute the values of x and y into the equation to determine the slope
-2 = m(-6) -5
Add 5 to each side
-2+5 =-6m
3 = -6m
Divide by -6
3/-6 = m
The slope is -1/2
y = -1/2 x -5
Where is Point B on the number line
Answers
Answer:
the answer is the second option
Step-by-step explanation:
it is
MATH HELP PLEASE !!! Due soon !!!
Answers
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.
A ruler can be used. It is easier if it combines full- and half-scale markings on the same edge. This will let you find the midpoint of a side quickly.
With a compass and straightedge, the usual process of constructing the bisector of a line segment is used.
A) m + n
B) 0
C) m - 1
D) -(m+n)
Answers
Answer:
D
Step-by-step explanation:
Lsh=rhs
U solve using algebra
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Answers
Answer:
Step-by-step explanation:
We could invent set B: {-2, 1, 3, 5, 6, 10} and then correctly state tht set A is a subset of B, because {-2, 1, 3} is also found in A.
Which system of equations has infinitely many solutions?
Answers
Which of the following segments is a diameter of O?
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
The diameters are
DE and AB
They can also be written as
ED and BA
Answer:
option A : AB
Step-by-step explanation:
The diameter is the length of the line through the center that touches two points on the edge of the circle.
Both AB and DE are diameters.
Therefore, Option A : AB
Find the Pythagorean triplets whose one number is 24.
Answers
Answer:
25, 24, 7
Step-by-step explanation:
can someone pls pls help me?
Answers
Answer:
its 30 or 24
Step-by-step explanation:
but its most likely 30
Math help please I will give brainlist if correct
Answers
Answer:
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im stumped by e srry
Which expression is equivalent to m² - 13m - 30?
Answers
Answer:
[tex](m−15)(m+2)[/tex]
Step-by-step explanation:
[tex] m² - 13m - 30?[/tex]
Formula :
[tex] {x}^{2} +bx+c[/tex]
[tex](m−15)(m+2)[/tex]
Hope it is helpful...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?
A. f−1(x) = 2x − 50
B. f−1(x) = 2x + 50
C. f−1(x) = 0.5x − 50
D. f−1(x) = 0.5x + 50
Answers
PLEASE HELP!! Which variable is most important to the following problem?
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
Jackie with 9 minutes left in the game. If each half is 16 minutes long, how
long did Jackie play?
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
Answers
Answer:
Step-by-step explanation:
d
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:
Por definición de razones trigonométricas, tenemos las siguientes identidades:
[tex]\tan \theta = \frac{y}{x} = \sqrt{2}[/tex] (1)
[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:
[tex]\sin \theta = \frac{\sqrt{2}}{\sqrt{5}} = \sqrt{\frac{2}{5} }[/tex]
[tex]\sin \theta = \frac{\sqrt{10}}{5 }[/tex]
[tex]\cos \theta = \sqrt{\frac{1}{5} }[/tex]
[tex]\cos \theta = \frac{\sqrt{5}}{5}[/tex]
Por último, calculemos [tex]A[/tex]:
[tex]A = 3\cdot \left(\frac{\sqrt{10}}{5} + \frac{\sqrt{5}}{5} \right) - \sqrt{7}[/tex]
[tex]A \approx 1.488[/tex]
Work out m and c for the line: y = 4 x − 1
Answers
Answer:
m=4 and c=-1
Step-by-step explanation:
I'm assuming that m is the slope and c is the y-intercept. (If this is not the case, please tell me and I'll fix my answer).
The equation is already in the form y=mx+c so you just take the numbers from the problem y=4x-1.
Answer:
m = 4 c=-1
Step-by-step explanation:
The slope form is y = mx + b.
M is the slope which is 4.
B is the y=intercept which is -1.
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]
Hehehejdjkskjsknssnnsnajsbsb
Answers
Answer:
10
Step-by-step explanation:
Wich Type of rectangle has not equal side lengths A. Isosceles B. Equilateral C. Scalene D. None of the above
Answers
Answer:
C. Scalene triangle
Step-by-step explanation:
Wich Type of triangle has not equal side lengths A. Isosceles B. Equilateral C. Scalene D. None of the above
scalene triangle can be regarded as triangle whereby all three sides of the triangle have different lengths. the angles in scalene triangle is also
different if measured. Some right triangles can as well be regarded as scalene triangle if other two angles( the legs) are not congruent. It should be noted that Type of triangle which has not equal side lengths is Scalene
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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Related Questions (More Answers Below)
I'll give brainliest!
Answers
Step-by-step explanation:
Answer:
D. 4 And 8
#Carryonlearning
Answer:
B
Step-by-step explanation:
If 50 kg of rice cost Rs 375,how much can be purchased for Rs.525?
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
Rice ( kg) Cost (Rs)
50 375
x 525
[tex]\frac{50}{x} = \frac{375}{525} \\\\x \times 375 = 50 \times 525\\\\375x = 26250\\\\x = \frac{26250}{375} = 70 \ kg[/tex]
Therefore 70kg rice can be purchased for Rs. 525
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Answers
2. 3, 1 and then 2
3.a
4. b