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
How long will it take to fill the tank with 40 gallons of water?
Answers
Answer:
15-25
Step-by-step explanation:
A ship leaves port at 1 pm traveling north at the speed of 30 miles/hour. At 3 pm, the ship adjusts its course on a bearing of N 20º E. How far is the ship from the port at 4pm?
Answers
No Solutions 2x + 5 + 2x + 3x = One Solution 2x+5+ 2x + 3x = Infinitely Many Solutions 2x + 5 + 2x + 3x =
Answers
Answer:
2x+5+2x +3x=7x+5 2x +5+ 2x + 3x = 7x+5
Step-by-step explanation:
Can someone please teach me long division, and please provide examples.
i haven't done long division in so long and i need to sharpen up.
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oh yea 50 points each.
Answers
Answer:
Step-by-step explanation:
Divide the tens column dividend by the divisor.
Multiply the divisor by the quotient in the tens place column.
Subtract the product from the divisor.
Bring down the dividend in the ones column and repeat.
okay so look at the image down below
Choose two pairs of alternate interror angles.
Answers
Answer: angle 5 and angle 10
angle 8 and angle 11
hope this helps!
Plz help I’m dumd and I can’t answer it
Answers
Answer:
11
Step-by-step explanation:
25% is 0.25 or 1/4
44 x 0.25 =11
1138 in expanded form
Answers
Answer:
(see below)
Step-by-step explanation:
To put 1138 in expanded form, you should first know that expanded form is separating a number into its place values. Here's what I'm talking about:
1 in expanded form is 1.
11 in expanded form is (10 + 1).
111 in expanded form is (100 + 10 + 1).
So that means that:
1138 in expanded form is (1000 + 100 + 30 + 8).
Please help me? I’ll give brainliest
Answers
Answer:
left 4 up one because the coordinates are -4 , 1
Answer:
the first one (-4, 1)
Step-by-step explanation:
- Question 11
Mrs. Pitoya has 30 apples and is buying more apples in crates containing 20 apples each. She needs 130 apples for a harvest celebration at her school,
Which equation and solution correctly represent x, the number of crates of apples Mrs. Pitoya needs to buy?
Answers
Answer:
Mrs pitoya has to buy 9 crates of apples
Answer: She only needs to buy 5 more crates of apples.
30 + 20(x) = 130
30-30+20(x)=130-30
20x = 100
x = 5
Step-by-step explanation:
To complete a task in 15 days, a company has 4 people each working 8 hours a day. The company
decide to have 5 people each working 6 hours a day. Assume that each person works at the same
rate.
a) How many days will it take the 5 people to complete the task?
b)Comment on how the assumption affects your answer to part (a).
Answers
Answer:
Let's suppose that each person works at an hourly rate R.
Then if 4 people working 8 hours per day, a total of 15 days to complete the task, we can write this as:
4*R*(15*8 hours) = 1 task.
Whit this we can find the value of R.
R = 1 task/(4*15*8 h) = (1/480) task/hour.
a) Now suppose that we have 5 workers, and each one of them works 6 hours per day for a total of D days to complete the task, then we have the equation:
5*( (1/480) task/hour)*(D*6 hours) = 1 task.
We only need to isolate D, that is the number of days that will take the 5 workers to complete the task:
D = (1 task)/(5*6h*1/480 task/hour) = (1 task)/(30/480 taks) = 480/30 = 16
D = 16
Then the 5 workers working 6 hours per day, need 16 days to complete the job.
b) The assumption is that all workers work at the same rate R. If this was not the case (and each one worked at a different rate) we couldn't find the rate at which each worker completes the task (because we had not enough information), and then we would be incapable of completing the question.
The ratio of teachers to students at Priory School is 2:27
What is school's total population if there are 42 staff
Answers
Answer:
609
Step-by-step explanation:
ratio of teachers to students at Priory School =2:27
Let X= total number of both the students and the teacher
Ratio of teacher=( 2/29)X
Ratio of student is (27/29 )X
But total number of teacher = 42
2/29 ×X =42
2X= 42×29
2X=1218
X= 609
Hence, school's total population is 609
Identify the figure below. Select all names that apply.
Image shows a four-sided figure with opposite sides parallel and equal in length.
A.
quadrilateral
B.
parallelogram
C.
rhombus
D.
square
E.
trapezoid
Answers
Answer:
b and d
Step-by-step explanation:
f(x) = -4x2 + 10
Find f(-2)
Answers
Answer:
f(-2) = -6
Step-by-step explanation:
In the expression, to get f(-2);
we simply substitute the value of x with -2
We have this as;
f(-2) = -4(-2)^2 + 10
f(-2) = -4(4) + 10
f(-2) = -16 + 10
f(-2) = -6
On a highway, a random sample is taken of the speed, in mph, of 50 cars. A mean speed of 61.8 mph is calculated with a margin of error of +2.3 for a 95% confidence interval What is the interval estimate of the population mean?
A) 58.7 <h<64.9
B)59.5<h<61.8
C)59.5<h<64.1
D)61.8<h<64.1
Answers
The interval estimate of the population mean when a random sample is taken of the speed on highway is 59.5<h<64.1. Option C is correct.
What is margin of error?The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.
The interval estimate of the population mean can be found out using the following formula:
[tex]\overline X\pm MOE[/tex]
Here, [tex]\overline X[/tex] is the average mean, and the MOE is the margin of error.
On a highway, a random sample is taken of the speed, in mph, of 50 cars.
A mean speed is 61.8 mphThe margin of error is +2.3 The confidence interval is 95%Put the values in the above formula as,
[tex]61.8\pm 2.3\\59.5,641[/tex]
Thus, the interval estimate of the population mean
[tex]59.5 < h < 61.8[/tex]
Hence, the interval estimate of the population mean when a random sample is taken of the speed on highway is 59.5<h<64.1. Option C is correct.
Learn more about the margin of error here;
https://brainly.com/question/10218601
#SPJ2
Subtract. Express your answer in lowest terms.
8 1/2 - 2 1/6
Answers
Answer:
[tex]6\frac{1}{3} or \frac{19}{3}[/tex]
Step-by-step explanation:
Rewriting our equation with parts separated
=8+1/2−2−1/6
Solving the whole number parts
8−2=6
Solving the fraction parts
1/2−1/6=?
Find the LCD of 1/2 and 1/6 and rewrite to solve with the equivalent fractions.
LCD = 6
3/6−1/6=2/6
Reducing the fraction part, 2/6,
2/6=1/3
Combining the whole and fraction parts
6+1/3=6 1/3
Simplify by expressing with radicals. ^6radical x^2 y^6
Answers
Suppose that 20% of students at high school A and 18% of students at high school B participate on a school athletic team. Independent random samples of 30 students from each school are selected and asked if they participate on a school athletic team. Let ˆ p A represent the sample proportion of students at school A who participate on a school athletic team and ˆ p B represent the sample proportion of students at school B who participate on a school athletic team.
What is the mean of the sampling distribution of ˆ p A − ˆ p B ?
Answers
Answer:
0.02
Step-by-step explanation:
High schools A :
Percentage of participants in on the school athletic team = 20%
Pa = 20% = 0.2
High school B:
Percentage of participants in on the school athletic team = 18%
Pa = 18% = 0.18
The mean of sampling distributon is :
Pa - Pb
0.2 - 0.18
Hence, Mean of sampling distribution is 0.02
Will give brainlist! The area of a swimming pool covers 350 square feet if the height of the pool if 5 feet what is the volume.
Answers
. 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
There are 15 students not going on the field trip. That is 6% of all
of the 6th graders, How many 6th graders are there?
Answers
Answer:
250
Step-by-step explanation:
15=6%
?=1%
15/6=2.5
2.5=1%
1%=1/100
2.5 x 100=
250
What does prime factorization mean to you ?
Answers
Answer:
Prime factorization is finding prime number that are multiply together to make the original number.
Step-by-step explanation:
One of the legs of a right triangle measures 1 cm and its hypotenuse measures 8 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answers
Answer:
about 7.8
Step-by-step explanation:
a^2+b^2=c^2
1^2+b^2=8^2
2+b^2=64
B^2=62
B= about 7.8
PLEASE NOTICE, IF YOU HELP ILL GIVE 50 POINTS AND BRAINLIEST
Answers
Answer:
See proof below.
Step-by-step explanation:
Statements Reasons
1. Seg. DE congr seg GF 1. Given
2. <1 congr. <2 2. Given
3. DE || GF 3. Theorem: If 2 lines are cut by a transversal such that alt int angle are congruent, then the lines are parallel
4. DEFG is a parallelogram 4. Theorem: If a quadrilateral has two sides that are congruent and parallel, then it is a parallelogram.
17. The base of a parallelogram is 10 meters. The height is one fourth of the base. Find the area of the parallelogram.
pleaaeee help
Answers
Answer:
25m2
Step-by-step explanation:
b = 10
10 divided by 4 = 2.5
h = 2.5
2.5 times 10 = 25m2
Nicole's school is selling tickets to a play. On the first day of ticket sales the school sold 3 senior
citizen tickets and 14 student tickets for a total of $232. The school took in $230 on the second day by selling 11 senior citizen tickets and 7 student tickets. Find the price of a senior citizen ticket and the price of a student ticket
100 points
Answers
Answer:
→ please refer to the above attachment ←
★ Cost of senior ticket is $12.★ Cost of student ticket is $14.SOMEBODY HELP PLZ IM STUCK
Answers
Please help me. You will be marked brainliest.
Answers
Answer:
What do you need help with?
Step-by-step explanation:
A glass vase factory recently produced 4 vases that were chipped and 16
vases that were not. Considering this data, how many of the next 10 vases
would you expect to be chipped?
Answers
Answer:
2
Step-by-step explanation:
4 chipped + 16 not chipped = 20 total
4 / 20 = 1/5 or 20% chance that vase will be chipped
Set up a proportion or find 20% of 10.
[tex]\frac{1}{5} = \frac{x}{10}[/tex] x = 2 (ten is on denominator because it's the total amount of vases)
or 10 * 0.2 = 2
CAN SOMEONE PLEASE HELP ITS EASY BUT IM D U M B
Answers
Answer:
I believe the answer is C. Use Desmos and plug in the equation y=-x-2
Step-by-step explanation:
40% of the people at Tim's Halloween party dressed up as superheroes. If 14 people dressed as superheroes, how many people were at Tim's Halloween party?
