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In the space below, use the law of sines or trigonometric ratios to find each length. Round your answer to 1 decimal place. (4 points total: 1 point each)
a. The length of the zip line, z
b. The height of the point on the tree where the top of the ladder rests against it, h
c. The distance between the base of the ladder and the base of the tree, b
d. The distance between the base of the tree and the spot where the zip line is anchored to the ground, B
Answers
Trigonometric ratios are useful in calculating the side lengths of a triangle.
The length of the zip line is 222.5 ftThe height where the ladder rests against the tree is 38.6 ftThe distance between the base of the ladder and that of the tree is 10.4 ftThe distance between the base of the tree and the spot where the zip line is anchored to the ground is 219.1 ft(a) Length, z
First we calculate (h) using the following sine ratio
[tex]\mathbf{sin(75) = \frac{h}{40}}[/tex]
Make h the subject
[tex]\mathbf{h = 40sin(75)}[/tex]
Next, we calculate (z) using the following sine ratio
[tex]\mathbf{sin(10)= \frac{h}{z}}[/tex]
Make z the subject
[tex]\mathbf{z= \frac{h}{sin(10)}}[/tex]
Substitute [tex]\mathbf{h = 40sin(75)}[/tex]
[tex]\mathbf{z= \frac{40sin(75)}{sin(10)}}[/tex]
[tex]\mathbf{z= 222.5 ft}[/tex]
Hence, the length of the zip line is 222.5 ft
(b) The height, h
In (a), we have
[tex]\mathbf{h = 40sin(75)}[/tex]
Evaluate
[tex]\mathbf{h = 38.6}[/tex]
Hence, the height where the ladder rests against the tree is 38.6 ft
(c) The distance, b
To do this, we make use of the following sine ratio
[tex]\mathbf{sin(15) = \frac{b}{40}}[/tex]
Make b the subject
[tex]\mathbf{b = 40sin(15)}[/tex]
[tex]\mathbf{b = 10.4}[/tex]
Hence, the distance between the base of the ladder and that of the tree is 10.4 ft
(d) Distance, B
To do this, we make use of the following sine ratio
[tex]\mathbf{sin(80) = \frac{B}{z}}[/tex]
Make B the subject
[tex]\mathbf{B = z\ sin(80)}[/tex]
Substitute [tex]\mathbf{z= 222.5 ft}[/tex]
[tex]\mathbf{B = 222.5\ sin(80)}[/tex]
[tex]\mathbf{B = 219.1}[/tex]
Hence, the distance between the base of the tree and the spot where the zip line is anchored to the ground is 219.1 ft
Read more about trigonometry ratios at:
https://brainly.com/question/24888715
The length of the zip line is 139.1 ft
The height where the ladder rests against the tree is 24.1 ft
The distance between the base of the ladder and that of the tree is 6.5 ft
The distance between the base of the tree and the spot where the zip line is anchored to the ground is 137.0 ft
(a) Length, z
First we calculate (h) using the following sine ratio
Sin(75)=h/25
Make h the subject
h=25sin(75)
Next, we calculate (z) using the following sine ratio
Sin(10)=h/z
Make z the subject
z=h/sin(10)
Substitute
h=25sin(75)
z= 25sin(75)/sin(10)
z=139.1 ft
Hence, the length of the zip line is 139.1 ft
(b) The height, h
In (a), we have
h=25sin(75)
Evaluate
h=24.1 ft
Hence, the height where the ladder rests against the tree is 24.1 ft
(c) The distance, b
To do this, we make use of the following sine ratio
sin(15)=b/40
Make b the subject
b=25sin(15)
b= 6.5 ft
Hence, the distance between the base of the ladder and that of the tree is 6.5 ft
(d) Distance, B
To do this, we make use of the following sine ratio
sin(80)=B/z
Make B the subject
B=z sin(80)
Substitute
z=139.1 ft
B=139.1 sin(80)
B=137.0 ft
Hence, the distance between the base of the tree and the spot where the zip line is anchored to the ground is 137.0 ft
Credit to the person above me for the format <3
Related Questions
<1 and <2 are complementary. Solve for the measure of <1.
<1 = 12x + 4
<2 = 9x + 2
A. 52
B. 4
C. 38
D. 8.3
Answers
Answer:
A) 52
Step-by-step explanation:
If < 1 and < 2 are complementary angles, then it means that the sum of their measures add up to 90°.
< 1 + < 2 = 90°
12x + 4 + 9x + 2 = 90°
21x + 6 = 90°
21x + 6 - 6 = 90° - 6
21x = 84°
21x/21 = 84°/21
x = 4
Substitute the value of x = 4 into < 1 and < 2:
m < 1: 12x + 4 = 12(4) + 4 = 52°
m < 2: 9x + 2 = 9(4) + 2 = 38°
Therefore, the correct answer is A) m < 1 = 52°.
What is the answer? Links will be reported. ( BRANLIEST )
Answers
Answer:
[tex] - 1 \frac{1}{8} m + \frac{3}{10} \\ [/tex]
Step-by-step explanation:
[tex] \frac{7}{8} m + \frac{9}{10} - 2m - \frac{3}{5} \\ \frac{7}{8} m - 2m + \frac{9}{10} - \frac{3}{5} \\ \frac{7}{8} m - \frac{2m \times 8}{1 \times 8} + \frac{9}{10} - \frac{3 \times 2}{5 \times 2} \\ \frac{7m - 16m}{8} + \frac{9 - 6}{10} \\ - \frac{9}{8} m + \frac{3}{10} \\ - 1 \frac{1}{8} m + \frac{3}{10} \\ [/tex]
IF YOU ARE REALLY GOOD A MATH THEN PLEASE ANSWER THIS !!!
Your help will be much appreciated because i am losing my sanity doing this math
Answers
Answer:
55mph
Step-by-step explanation:
average speed=330/6=55mph
newton's second law of motion States that the acceleration of an object is directly proportional to the force exerted on the object. if an object accelerates at a rate of 3 m/s2 , it will exert a force of 15 N. how much force will the same object exert if it accelerates at a rate of 7 m/s2?
pls pls pls help (๑•﹏•)
Answers
Answer:
Step-by-step explanation:
F=(2kg)×(3ms2). ∴F=6kgms2=6 Newton. =6N. Therefore, Force required to accelerate the body is 6N
The force the same object will exert if it accelerates at a rate of 7 m/s² is 35 N
From the question,
We have that,
Newton's second law of motion states that the acceleration of an object is directly proportional to the force exerted on the object
Let a represent the acceleration and F represent the force exerted
Them we can write that
F ∝ a
Introducing a constant, m, which is the mass of the object
Then, we get
F = ma
From the question,
If an object accelerates at a rate of 3 m/s² , it will exert a force of 15 N
We will the determine the mass, m, of the object using the above formula
F = ma
We have that
a = 3 m/s²
F = 15 N
Using
F = ma
Then,
15 = m × 3
m = 15÷3
∴ m = 5kg
Now, we can determine the force the same object would exert if it accelerates at at rate of 7 m/s²
Using the same formula
F = ma
a = 7 m/s²
m = 5 kg
∴ F = 5 × 7
F = 35 N
Hence, the force the same object will exert if it accelerates at a rate of 7 m/s² is 35 N
Learn more here: https://brainly.com/question/20357188
what is the slope of a line parallel to the line on the graph?
Answers
Answer:
3/4
Step-by-step explanation:
To find the slope of a line parallel to this line, we first need to find the slope of this line. Using rise/run, you get that the slope is 6/8 which simplifies to 3/4.
The slope of any two parallel lines always is the same so the slope of a line parallel to the one given would be 3/4.
HELPPPPPPPPPPPP PLEASEEEE
Answers
Answer:4
Step-by-step explanation:
6 ÷ 0.5 plss answer
Marking Brainliest!!
Answers
Answer:
12Step-by-step explanation:
0.5 = 1/2
6 ÷ 0.5 = 12
or
6 : 1/2 =
6 × 2 = 12
solve pls brainliest
Answers
Answer: (a.) -19 (b.) 78
Step-by-step explanation:
(a.) -33+14= -19 (b.) 75 - x = 78
(b.) 75 to zero = 75 Zero to -3
is 3 points behind zero, this make more distance from 75 so…
(b.) 75+3 = 78
simplify (-7b2)(-2b3)
Answers
Answer: 145
Step-by-step explanation:
(−72)(−23)
−72(−23)
1423
Alex‘s credit card balance is -$200 after a long she makes a payment of $50 towards her bill what integer represents
how much she still owes
Answers
Answer: 250
Step-by-step explanation:
i took a test
I NEED A 100% ACCURATE ANSWER FOR THIS QUESTION ASAP NO LINKS !!!
Answers
Answer:
The first choice
Step-by-step explanation:
h=-3
hope it helps
[tex]5h - 2 = 3h + 4 \\ = > 5h - 3h = 4 + 2 \\ = > 2h = 6 \\ = > h = \frac{6}{2} \\ = > h = 3[/tex]
Answer:Option d. 3
as part of a campaign to promote it's annual clearance sale
Answers
Answer:
is this a question or not?
Step-by-step explanation:
pls help i’m so confused
Answers
Answer:
I think your answer is i
Step-by-step explanation:
The rotational symmetry would be letters i
The letter with rotational symmetry is i
Can somebody help me asap I need this finished
Answers
Answer:
A) y=5x-3
Step-by-step explanation:
QUESTION: 3 ÷ 0.05
EMERGENCY: Pls answer
Answers
Step-by-step explanation:
=3/0.05
=60ans.
mark me as a brainlist plz.
the answer is 60
You can solve it in calculator
Josh bought seven boxes. A week later half of all his boxes were destroyed in a fire. There are now only 22 boxes left. With how many did he start? Please write an equation.
Answers
Answer:
Josh started out with 37 boxes.
Step-by-step explanation:
How many minutes is it before 12 noon if 68 minutes ago it was three times as many minutes past 10 a.m.?
Answers
x + 68 = 3 ×
×
(120 - x) →
→
x = 73 min
… if 68 minutes ago it (now) was three times as many minutes past 10 am (then)
x = 3 ×
×
[120 - (x + 68)] →
→
x = 39 min
… if 68 minutes ago it (then) was three times as many minutes past 10 am (then)
x + 68 = 3 ×
×
[120 - (x + 68)] →
→
x = 22 min
This graph represents 2x+y=−4.
Which ordered pair is in the solution set of 2x+y≤−4?
Question 6 options:
(2, −2)
(−2, −2)
(2, 2)
(−2, 2)
Answers
Answer:
(-2, -2)
Step-by-step explanation:
Select the correct answer. What is a round character? A. a character who contrasts the personality of another character B. a character who stays the same throughout a story C. a character who has a complex personality D. a character who has just one or two personality traits
Answers
What is the least five-digit even number with no repeated digits?
Answers
Winston ate 180 hot dogs in 9 hours. At that rate, how many hot dogs
would he eat in 12 minutes?
Answers
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
Step-by-step explanation:
The answer is B brace in this image it shows the words that it says plz trust me and tell me if this is wrong it should not be tho
While at School Brian had a math quiz every 6 days and a science quiz every four days. On February 15 he had both tests. Assuming no school days off when will he have both tests on the same day again.
Answers
Days x # of tests = days until both
6x2=12
4x3=12
[tex]-3\log_{3}\left(x-2\right)=-25[/tex]
Thanks!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!...........
Answers
[tex] - 3 log_{3}(x - 2) = - 25 \\ = > log_{3}(x - 2) = \frac{ - 25}{ - 3} \\ = > log_{3}(x - 2) = \frac{25}{3} \\ = > (x - 2) = ( \frac{25}{3} ) ^{3} \\ = > x - 2 = \frac{15625}{27} \\ = > x = \frac{15625}{27} + 2 \\ = > x = \frac{15625 + 54}{27} \\ = > x = \frac{15679}{27} \\ = > x = 5226.33[/tex]
Answer:
5226.33 (approximate value)
Hope you could get an idea from here.
Doubt clarification - use comment section.
(-10)-[9+(-3)]×2²÷(-8)
Answers
Answer:
-7
Step-by-step explanation:
Use the IQR to determine if any of the data in the data set are outliers.
{23,80,43,23,0,20,23,23,20,28}
Answers
Using the IQR, the only outlier in the data set is: 0.
What is the IQR of a Data Set?IQR = upper quartile (Q3) - lower quartile (Q1).
Given the data set, 23,80,43,23,0,20,23,23,20,28:
Quartile (Q1): 20
Quartile (Q3): 31.75
IQR = 31.75 - 20 = 11.75
The outliers are data values that lie below:
Q1 - (1.5 × IQR) = 20 - (1.5 × 11.75) = 2.375
And data values that are above:
Q3 + (1.5 × IQR) = 31.75 + (1.5 × 11.75) = 49.375
Therefore, the only outlier is: 0.
Learn more about the IQR on:
https://brainly.com/question/4102829
#SPJ1
4) Sally has 10 purple beads, 25 yellow beads and 30 red beads. She is
going to make identical bracelets for her friends. What is the maximum
number of bracelets she can make if she wanted to use all her beads?
Answers
Answer:
5 bracelets
Step-by-step explanation:
The common factor of 10, 25 and 30 is 5
this means that each bracelet will have 2 purple, 5 yellow and 6 red.
Answer:
5 Bracelets
Step-by-step explanation:
the common factor of the numbers 10 25 and 30 is 5
5×2= 10
5× 5 = 25
5x6= 30
these numbers are also multiples of 5.
I need some help with this
Answers
The following can be deduced from the expressions
m ∠ D = 4 × m ∠ A
m ∠ B = 3 × m ∠ A-12
Please note that the sum of angles in a triangle is 180 degress. Therefore,
M∠ A + m ∠ B + m ∠ D = 180equation(3)
Substitute for equation 1 and 2 in equation 3 as shown below
m ∠ A + 3 × m ∠ A - 12^0 + 4 x m ∠ A =180^0
m ∠ A + 3 × m ∠ A + 4 x m ∠ A = 180^0+12^0
8m ∠ A = 192^0
m ∠ A= 192^0/8
m ∠ A=24^0
Substitute for m∠A= 24 in equation 1 and 2 as shown below
m ∠ D = 4 × m ∠ A
m ∠ D = 4 × 24^0
m ∠ D = 96^0
m ∠ B = 3 × mA - 12^0
m ∠ B = 3 × 24^0 - 12
m ∠ B = 72^0 - 12^0
,
∠= °
∠= °
∠= °
HELPS! TYS IF U DOESSSSS
I WILL GIVE BRAINILEST!!!!!!!!!
Answers
Answer:
C. HI my other account:P
Step-by-step explanation:
Can someone please show a piece of paper or ex’s plum how you do h point?
Answers
Answer:
(-1,-1)
Step-by-step explanation:
well a square has four sides and they are all equal so it would have to be (-1,-1) for the sides to be equal