Because of prevailing winds, a tree grew so that it was leaning 6º from the vertical. At a point d = 37 meters from the tree, the angle of elevation to the top of the trees
is a = 29° (see figure). Find the height h of the tree. (Round your answer to one decimal place.)
h =
m
d m
Additional Materials
eBook
Answers
Answer:
Height of the tree is 40.0 meters.
Step-by-step explanation:
From ΔABC,
m∠ABC = 90°
Since, m∠ABC = m∠CBD + m∠ABD
90° = 6° + m∠ABD
m∠ABD = 90°- 6° = 84°
By triangle sum theorem in ΔABD,
m∠ABD + m∠BDA + m∠DAB = 180°
84° + 29° + m∠BDA = 180°
m∠BDA = 180° - 113°
= 67°
By sine rule in ΔABD,
[tex]\frac{\text{sin}(\angle BDA)}{d}= \frac{\text{sin}(\angle ABD)}{h}[/tex]
[tex]\frac{\text{sin}(67)}{37}= \frac{\text{sin}(84)}{h}[/tex]
h = [tex]\frac{\text{sin}(84)\times 37}{\text{sin}(67)}[/tex]
h = 39.98
h ≈ 40.0 meters
Therefore, height of the tree is 40.0 meters.
The sine rule is the ratio of the side length to the sine of the opposite angles. Then the height of the tree is 40 meters.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a triangle.
Because of prevailing winds, a tree grew so that it was leaning 6º from the vertical.
At a point d = 37 meters from the tree, the angle of elevation to the top of the trees is a = 29° (see figure).
∠ABC = 90
We have
In ΔABC
∠ABC = ∠CBD + ∠ABD
∠ABD = 90 - 6
∠ABD = 84
By triangle sum in ΔABD, we have
∠ABD + ∠BDA + ∠DAB = 180
∠BDA = 180 - 84 - 29
∠BDA = 67
Then by the sine rule, we have
[tex]\begin{aligned} \dfrac{\sin \angle BDA}{d} &= \dfrac{ \sin \angle ABD }{h}\\\\\dfrac{\sin 67}{37} &= \dfrac{\sin 84}{h}\\\\h &= \dfrac{\sin 84} \times 37{\sin 67}\\\\h &= 39.98 \approx 40 \end{aligned}[/tex]
More about the trigonometry link is given below.
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
The standard equation of a line in point slope form is expressed as;
y -y0 = m(x-x0)
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Get the slope
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Answer:
1. b
2. c
3. d
4. a
5. e
Step-by-step explanation:
When the equation is written in slope-intercept form of ;
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Answers
Nina's grandmother earn $288.75 interest after 21 months.
What is Simple interest?
The cost of borrowing money without accounting for the effects of compounding is called Simple interest.
Given that;
Principal amount (P) = 3,000
Rate (R) = 5.5%
Time (T) = 21 month = 1 9/12 years
Now, The formula for the interest is;
Interest = P × R × T / 100
Where, P is the principal amount of money, R is the interest rate, T is the time.
Substitute all the values we get;
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= 55 × 21 / 4
= 288.75
Thus, Nina's grandmother earn $288.75 interest after 21 months.
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Answers
Answer: x = -27
Step-by-step explanation:
Answer:
x=-27Step-by-step explanation:
to understand thisyou need to know about:equationPEMDASgiven:[tex] - 8 = \frac{x}{3} + 1[/tex]to solve[tex]x[/tex]let's solve:[tex] step - 1 : define \\ - 8 = \frac{x}{3} + 1[/tex]
[tex]step - 2 : \\ rewrite[/tex]
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[tex]step - 3 : \\ subtract \: 1 \: from \: both \: sides[/tex]
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Answers
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А. 4 x 10^5
B. 9 x 10^4
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Answers
Answer:
i think b
Step-by-step explanation:
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As per option (A),
4 x 10⁵
This number is not a square number.
As per option (B),
9 x 10⁴ = (3² x 10²)²
This number is a square number.
As per option (C),
4 x 10³
This number is not a square number.
As per option (D),
9 x 10³
This number is not a square number.
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
2^6
Step-by-step explanation:
The equivalent of the expression, 2 x 2 x 2 x 2 x 2 x 2 is 2⁶.
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An equivalent expression is an expression that has the same value or worth as another expression, but does not look the same.
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Answer:
Step-by-step explanation:
51
Answer:
17x3=51
Step-by-step explanation:
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You are going to a fair! It costs $6 for the
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Answers
Answer:
5
Step-by-step explanation:
21-6=15/3=5
Answer:
5 tickets
Step-by-step explanation:
21-6=16 16 divided by 3= 5.333 so about 5 tickets
Choose the best answer.
A beekeeper pays $30 to rent a booth at a farmers' market.
She charges $5 for each jar of honey. The graph shows this
situation, which is modeled by the equation y = 5x - 30.
Which of the following is true?
A. The value of x can be negative.
B. The value of y can be negative.
C. The value of x can be fractional.
D. The value of y cannot be zero.
X
Answers
Answer: The answer is A
Step-by-step explanation: because 5x-30= -150 because I looked it up
Answer:
B. The value of y can be negative.
Step-by-step explanation:
The value of y can be negative, which means the beekeeper wasn't able to sell a lot of jars that could compensate the amount he paid for the booth. It also means he didn't have any profit, rather, he incurred a loss.
For example, if the beekeeper sold only 5 jars of honey, the solution will look like this:
Let x be the number of jars of honey the beekeeper sold.
y = 5x - 30y = 5(5) - 30y = 25 - 30y = -5This means that the beekeeper has a loss of $5.
Kaya's family spends $105 to rent a boat for 7
days. The total cost, c, of the boat rental is
proportional to the number of days, d, the
family rents the boat.
с
e:
A. How much does it cost, in dollars, to
rent the boat for 3 days? SHOW
WORK!
B. Create an equation using "c" and "d" to
represent the proportional relationship
Answers
Answer:
A: $45 for 3 days
B: c=d(15)
Step-by-step explanation:
A: If 105 is the cost for 7 days and we want to find the cost for only 3 we have to find the cost for one day to start with so, 105 divided by 7 which is $15 so its 15 dollars a day then you multiply 15 by the number of days we want (3) and you get $45.
Test Prep Which of the following measurements is equivalent to 528 feet?
Select all the correct answers.
44 inches
6,336 inches
0.1 mile
176 yards
5,280 inches
Answers
Answer:
6,336 inches, 0.1 mile, and 176 yards
Step-by-step explanation:
I just looked it up lol
In Δ ABC and ΔXYZ ,∠B=∠X=90 and BC=XZ .What additional information is required to make Δ ABC congruent to ΔXYZ by R.H.S condition.
Answers
Answer:
AC = XY
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. The types of triangles are scalene triangle, equilateral triangle, right angled triangle and obtuse triangle.
Two triangles are said to be congruent if all the three sides and three angles of one triangle is equal to the three sides and three angles of the other triangle.
In Δ ABC and ΔXYZ ,∠B=∠X=90. This means that triangle ABC and triangle XYZ are right angled triangle since one of their angles is 90 degrees.
The hypotenuse is the side opposite to right angle (90 degrees).
Therefore AC is the hypotenuse of triangle ABC and YZ is the hypotenuse of triangle XYZ.
If the hypotenuse and one leg of a right angled triangle is equal to the hypotenuse and leg of another right angled triangle, then the two triangles are congruent by RHS rule.
Since BC = XY, for Δ ABC congruent to ΔXYZ by R.H.S condition, the hypotenuse have to be equal, i.e. AC = XY
In the function y= 1/3x^2,
what effect does the number 1/3 have on the graph,
as compared to the graph of the function y= x^2
A. It stretches the graph horizontally by a factor of 3.
B. It shrinks the graph horizontally to 1/3 its original width.
C. It shrinks the graph vertically to 1/3 its original height.
D. It stretches the graph vertically by a factor of 3.
Answers
If a line passes through (4,13) and (6,19) what is the slope? And can you please explain how you got your answer
Answers
Answer:
The slope is 3.
Step-by-step explanation:
The equation for slope is either [tex]\frac{y2-y1}{x2-x1}[/tex] or [tex]\frac{y1-y2}{x1-x2}[/tex]. So this should be [tex]\frac{19-13}{6-4}[/tex], which is 3.
Answer:
Slope =
6
—
2
Step-by-step explanation:
First find the rise over run
Second use the format
Y2-y1
———-
X2-x1
Using the format you will get this
19-13
——
6-4
Next solve
Which then you get
6
—
2
Using the graph above identify the constant of proportionality between the number of shirts and how much they cost? Hint: simplify your answer
A. K=80
B. K=20
C. K=10
D. k=8
Answers
Answer:
We conclude that the constant of proportionality between the number of shirts and how much they cost is:
k = 8
Hence, option 'D' is correct.
Step-by-step explanation:
We know that when 'y' varies directly with 'x', we get
y ∝ x
y = kx
k = y/x
where k is called the constant of proportionality
Given the points
(10, 80)(20, 160)(50, 400)For (10, 80)
substituting y = 80 and x = 10 in the equation
k = y/x
k = 80/10 = 8
For (20, 160)
k = y/x
k = 160/20 = 8
For (50, 400)
k = y/x
k = 400/50 = 8
It is clear that the value of k is the same for all the points.
Thus, the value of k = 8
Therefore, we conclude that the constant of proportionality between the number of shirts and how much they cost is:
k = 8
Hence, option 'D' is correct.