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.
https://brainly.com/question/22698523
Related Questions
what is the solution to the equation below?
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]
[tex]\frac{x}{3} + 1= - 8[/tex]
[tex]step - 3 : \\ subtract \: 1 \: from \: both \: sides[/tex]
[tex] \frac{x}{3} + 1 - 1 = - 8 - 1[/tex]
[tex] \frac{x}{3} = - 9[/tex]
[tex]step - 4 : \\ multiply \: both \: sides \: by \: 3[/tex]
[tex] \frac{x}{3} \times 3 = - 9 \times 3[/tex]
[tex] \huge \therefore x = - 27[/tex]
Given m∥n the value of x. (8x-20) (8x+8)
Answers
c) Which of these numbers is a square number?
А. 4 x 10^5
B. 9 x 10^4
C. 4 x 10^3
D. 9 x 10^3
Answers
Answer:
i think b
Step-by-step explanation:
9=3^2 and 10^4=(10^2)2
The number 9 x 10⁴ is a square number. which the correct answer would be an option (B).
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
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.
Thus, the number 9 x 10⁴ is a square number.
Hence, the correct answer would be option (B).
Learn more about the number system here:
https://brainly.com/question/21751836
#SPJ2
17 x 3 1st grade on me homwok i need now
Answers
Answer:
Step-by-step explanation:
51
Answer:
17x3=51
Step-by-step explanation:
A bakery is filling an order for 180 cupcakes. Jeff has baked and
decorated 75% of the cupcakes. How many cupcakes has been baked
and decorated?
Answers
Answer:
135 cupcakes
Step-by-step explanation:
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.
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
Please answer with all steps!
Will give brainleist
Answers
Answer:
x = 109
Step-by-step explanation:
x and 109° are vertically opposite angles and are congruent, so
x = 109
How do you graph this? y=−5x
Answers
Answer:
Step-by-step explanation:
dont need to graph the center dot, its just the origin
A child. Should no longer use a boister seat when they reach 4'9" tall Janet is 59 inches tall. Can she go without a booster seat
Answers
Answer:
Yes she can. 59 is 4.9 feets
Step-by-step explanation:
searched it on goog
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
PLEASE HELP 15 POINTS
An item costs $420 before tax, and the sales tax is $16.80 .
Find the sales tax rate. Write your answer as a percentage.
Answers
Answer:
The sales tax is 4%
Step-by-step explanation:
hope this helps plz mark brainliest
You are going to a fair! It costs $6 for the
admission. Each ride costs $3. You have
$21. How many ride tickets can you buy? I need to know fast!
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
The point (x, y) is proportional to the point (2, 5).
Select all the true statements.
A. (x,y) is a solution to y=5/2x.
B. (x, y) is a solution to y=x+3.
C. The ratio of is equivalent to 5/2:
D. Point (x,y) is the same point as (5,2).
E. A straight line through points (2, 5) and (x,y) will pass through the origin.
Answers
Answer:
did u get the answer??
Step-by-step explanation:
if so plz help
Anyone know the correct answer?!
Answers
Answer: Lower-right corner [tex]3^7 \times \frac{1}{3^4}[/tex]
Explanation:
We use the rule that
[tex]a^{-b} = \frac{1}{a^b}[/tex]
The negative exponent tells us to apply the reciprocal if we want the exponent to be positive.
In this case, a = 3 and b = 4
So,
[tex]a^{-b} = \frac{1}{a^b}\\\\3^{-4} = \frac{1}{3^4}[/tex]
which is why overall,
[tex]3^7\times 3^{-4} = 3^7 \times \frac{1}{3^4}[/tex]
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
Write an equivalent expression for 2 x 2 x 2 x 2 x 2 x 2
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.
How to find an equivalent expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
An equivalent expression is an expression that has the same value or worth as another expression, but does not look the same.
Therefore, let's simplify the expression to find its equivalent as follows:
2 x 2 x 2 x 2 x 2 x 2 = 2⁶
learn more on expression here: brainly.com/question/111385
#SPJ6
55.563 to the nearest hundredths
Answers
Answer:55.56
Step-by-step explanation:
the 6 is in the hundreds place
the number to the right is below 5 therefore the 6 will stay the same
hope this helps
. At a farmer’s market, two vendors sell fresh milk. One vendor sells 2 liters for $3.80, and another vendor sells 1.5 liters for $2.70. Which is the better deal? *
Answers
Answer: 1.5 liters
Step-by-step explanation:
3.80 divided by 4= 0.95 0.95 x 3= 2.85
2.85 is more than 2.70
mark me brainliest
Solve for x.
6
х
12
15
X=
units
Answers
Answer:
x = 4
Step-by-step explanation:
If a line is parallel to a side of the triangle and intersects the other 2 sides then it divides those sides proportionally, that is
[tex]\frac{2}{4}[/tex] = [tex]\frac{x-1}{6}[/tex] ( cross- multiply )
4(x - 1) = 12 ( divide both sides by 4 )
x - 1 = 3 ( add 1 to both sides )
x = 4
Write the equation of a line through (-1,-5) parallel to 3x-y=5, and in slope intercept form
Answers
Answer:
y =3 x
Step-by-step explanation:
The standard equation of a line in point slope form is expressed as;
y -y0 = m(x-x0)
m is the slope
(x0, y0) is the point on the line
Given the line 3x - y = 5
Get the slope
- y = -3x + 5
y = 3x - 5
Slope m = 3
Substitute m = 3 and (-1, -5) into the given formula
y - (-5) = 3(x-(-1))
y+5 = 3(x+1)
y + 3 = 3x+3
y = 3x + 3 - 3
y = 3x
Hence the equation in slope intercept form is y =3 x
Put a digit in the gap, such that the answer is a whole number:
e
9x - 94-10...
Answers
The numbers that make the result a whole number are 20 for x and 2 for the gap number.
How to identify the number that needs to be added?The first step would be to identify the result of this expression and then add the number that can make this result a whole number.
9x - 94-10__9x - 104 (negative numbers are not whole numbers, the result must be a positive number)Based on this, the possible values for x and the number in the gap are:
x= 20 Gap = 29(20) - 94 -10(2)180 - 94 -20180 - 11466 - This is a whole number.Learn more about Numbers in: https://brainly.com/question/17429689
Shaniah is charging the Johnson family to walk their dogs. She charges $80 a week
and they pay her a 9% tip each week. How much is Shaniah's tip? How much total
money does Shaniah make?
Answers
Answer:
89
Step-by-step explanation:
Nina's grandmother deposits 3000 into a saving account for her account pays 5.5% simple interest on an annual basis if she does not add or withdraw money from the account how much interest will she earn after 21 months round to the nearest tenth
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;
Interest = 3,000 × 5.5 × 1 9/12 / 100
= 55 × 21 / 4
= 288.75
Thus, Nina's grandmother earn $288.75 interest after 21 months.
Learn more about the simple interest visit:
https://brainly.com/question/20690803
#SPJ5
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
What is the solution of the system? {5x−y=−21x+y=−3 Enter your answer in the boxes. ( , )
Answers
Answer:
(-4,1)
Step-by-step explanation:
im pretty sure that is the answer, i will finish the test and tell you if it is right in the comments i guess lol
Answer:
(-4,1)
Step-by-step explanation:
I took the test
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.
HELP I NEED HELP ASAP
Answers
ANYONE PLEASE HELP ME MATCH THESE I DONT GET IT AND HAVE 1 MINUTE LEFTTT
Answers
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 ;
y = mx + b, then m is the slope and b is the y-intercept
In this case;
1. y= -7/6x + 1 --------- m= -7/6 ; b = 1 --------b
2. y=7/6x -1 ------------m = 7/6 ; b = -1 ---------c
3. y= x-7/6 -------------m = 1 ; b = -7/6 ---------d
4. y= -x -7/6 ----------m =-1 ; b = -7/6 ----------a
5. -x + 6/7 ------------m = -1 ; b = 6/7---------e
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.