An evergreen tree is supported by a wire extending from 1.5 feet below the top of the tree to a stake in the ground. The wire is 24 feet long and forms a 58° angle with the ground. how tall is the tree?
Answers
Answer:
Approximately [tex]21.9\; \rm ft[/tex] (assumption: this tree is perpendicular to the ground.)
Step-by-step explanation:
Refer to the diagram attached (not drawn to scale.)
Label the following points:
[tex]\rm S[/tex]: stake in the ground.[tex]\rm A[/tex]: top of the tree.[tex]\rm B[/tex]: point where the wire is connected to the tree. [tex]\rm C[/tex]: point where the tree meets the ground.Segment [tex]\rm SB[/tex] would then denote the wire between the tree and the stake. The question states that the length of this segment would be [tex]24\; \rm ft[/tex]. Segment [tex]\rm AB[/tex] would represent the [tex]1.5\; \rm ft[/tex] between the top of this tree and the point where the wire was connected to the tree.
The question is asking for the height of this tree. That would correspond to the length of segment [tex]\rm AC[/tex].
If this tree is perpendicular to the ground, then [tex]\rm \angle A\hat{C}S =90^\circ[/tex]. Triangle [tex]\rm \triangle BCS[/tex] would be a right triangle with segment [tex]\rm SB[/tex] as the hypotenuse.
The question states that the angle between the wire (segment [tex]\rm SB[/tex]) and the ground (line [tex]\rm SC[/tex]) is [tex]58^\circ[/tex]. Therefore, [tex]\rm \angle A\hat{S}C = 58^\circ[/tex].
Notice, that in right triangle [tex]\rm \triangle BCS[/tex], segment [tex]\rm BC[/tex] is the side opposite to the angle [tex]\rm \angle B\hat{S}C = 58^\circ[/tex]. Therefore, the length of segment [tex]\rm BC\![/tex] could be found from the length of the hypotenuse (segment [tex]\rm SB[/tex]) and the cosine of angle [tex]\rm \angle B\hat{S}C = 58^\circ\![/tex].
[tex]\displaystyle \cos\left(\rm \angle B\hat{S}C\right) = \frac{\text{length of $\mathrm{BC}$}}{\text{length of $\mathrm{SB}$}} \quad \genfrac{}{}{0em}{}{\leftarrow\text{opposite}}{\leftarrow \text{hypotenuse}}[/tex].
Rearrange to obtain:
[tex]\begin{aligned}& \text{length of $\mathrm{BC}$} \\ &= (\text{length of $\mathrm{SB}$}) \cdot \cos\left(\angle \mathrm{B\hat{S}C}\right)\\ &= \left(24\; \rm ft\right) \cdot \cos\left(58^\circ\right) \approx 20.35\; \rm ft\end{aligned}[/tex].
In other words, the wire is connected to the tree at approximately [tex]20.3\; \rm ft[/tex] above the ground.
Combine that with the length of segment [tex]\rm AB[/tex] to find the height of the entire tree:
[tex]\begin{aligned}&\text{height of the tree} \\ &= \text{length of $\mathrm{AC}$} \\ &= \text{length of $\mathrm{AB}$} + \text{length of $\mathrm{BC}$}\\ &\approx 20.35\; \rm ft + 1.5\; \rm ft \\ &\approx 21.9\; \rm ft\end{aligned}[/tex].
Related Questions
HELP!
during a back to school sale, a store sold jeans at a 25% discount. if one pair of jeans originally cost $35, what was its price during the sale?
Answers
Answer:
15$
Step-by-step explanation:
hope this helped
Answer:
35*0.25= 8.75 (multiply by the discount converted into a decimal)
35- 8.75= 26.25 (subtract that from the original to find the discount price)
or
35* 0.75= 26.25 (multiply by the percentage of the original price that you bought the jeans at)
Step-by-step explanation:
either way the answer is $26.25 is the discounted price
Evaluate 32 divided by 1.6
show work
Answers
Answer:
20
Step-by-step explanation:
32/1.6= 20
How do you want me to show the work? Long division?
Answer:
20
Step-by-step explanation:
Idk how you want me to show the work, sorry. The formatting will be weird unless I attach a pic or something
Geometry B Final Name Date Period Name the relationship. complementary, linear pair, vertical, adjacent, alternate interior, corresponding, or alternate exterior 1 2) 3) 4) 5) 6) 7) 8)
Answers
Answer:
but we can't write all the answers here
Answer:
Step-by-step explanation:
1. complementary
2. alt ext
3. supplementary
4. corresponding
5. b=65
6. 34
7. x=7
8.x=18
Solve x^2 +13x+12=0 Please answer this
Answers
Answer:
x=−1 or x=−12
Step-by-step explanation:
Let's solve your equation step-by-step.
x2+13x+12=0
Step 1: Factor left side of equation.
(x+1)(x+12)=0
Step 2: Set factors equal to 0.
x+1=0 or x+12=0
x=−1 or x=−12
Answer:
Solution
=
−
1
=
−
1
2
Step-by-step explanation:
I'm not 100 % sure about my answer
The heights of dogs, in inches, in a city are normally distributed with a population standard deviation of 7 inches and an unknown population mean. If a random sample of 20 dogs is taken and results in a sample mean of 21 inches, find a 95% confidence interval for the population mean. z0.10z0.10 z0.05z0.05 z0.025z0.025 z0.01z0.01 z0.005z0.005 1.282 1.645 1.960 2.326 2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.
Answers
Answer:
The 95% confidence interval is [tex] 17.932 < \mu < 20 + 22.068[/tex]
Step-by-step explanation:
From the question we are told that
The population standard deviation is [tex]\sigma =7 \ inches[/tex]
The sample size is n = 20
The sample mean is [tex]\= x = 20[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{7 }{\sqrt{20} }[/tex]
=> [tex]E = 2.068[/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 20 - 2.068 < \mu < 20 + 2.068[/tex]
=> [tex] 17.932 < \mu < 20 + 22.068[/tex]
can somebody help me with that
Given: GI¯¯¯¯¯¯¯ bisects ∠HGJ and ∠H≅∠J
Prove: △GIJ≅△GIH
Answers
Answer:
tbh how we suppose to help
Find the value of x.
Group of answer choices
25
40
65
115
Answers
Answer:
40
Step-by-step explanation
x=40 because if you time these in like this:
3(40)-10= 110
40+15=55
If you user 65 it'll be wrong because:
3(65)-10=185
And the whole thing is only 180 :]
if the nth term of a sequence is n^2 -3, find the first 3 terms and the 10th term.
Answers
Answer: -2, 1, 6,...97
Step-by-step explanation:
1st term: 1^2 - 3 = -2
1^2 = 1
1-3=-2
2nd term: 2^2-3 = 1
2^2 = 4
4-3=1
3rd term: 3^2-3 = 6
3^2 = 9
9 -3 = 6
10th term: 10^2-3 = 97
10^2 = 100
100-3=97
a.
[tex] \cot^{2} - \cos ^2a = \cot ^{2} a \times \cos ^{2} a[/tex]
Answers
Step-by-step explanation:
We need to prove that,
[tex]\cot^2 a-\cos^2 a=\cot^2 a\times \cos^2 a[/tex]
Taking LHS,
[tex]\cot^2 a-\cos^2 a[/tex]
We know that,
[tex]\cot a=\dfrac{\cos a}{\sin a}[/tex]
[tex]=(\dfrac{\cos a}{\sin a})^2 -\cos^2 a\\\\=\cos^2 a(\dfrac{1}{\sin^2 a}-1)\\\\=\cos^2 a(\dfrac{1-\sin^2a}{\sin^2 a})\\\\=\cos^2 a\times \dfrac{\cos^2 a}{\sin^2 a}\\\\=\dfrac{\cos ^2 a}{\sin^2 a}\times \cos^2a\\\\\because \ \dfrac{\cos ^2 a}{\sin^2 a}=\cot^2 a\\\\=\cot^2 a \times \cos^2a\\\\=RHS[/tex]
So, LHS = RHS
Hence, proved.
A new window costs $600 plus VAT 20%. How much is the total bill?
Answers
Answer:
720
Step-by-step explanation:
600*.2=120
120+600
720
Answer:
720 dollars
Step-by-step explanation:
find 20% of 600 dollars
[tex]\frac{20}{100} * 600[/tex]
= 120 dollars
600 + 120
= 720
I hope this helped!
please mark me as brainliest
The height in feet (h) of the ball t seconds after it is released can
be modeled using the formula: – 16t^2 + 10t + 6 = h
Find the time, in seconds, passed before the ball hits the ground
(let h = 0).*
*PLEASE SHOW WORKK
Answers
Step-by-step explanation:
h = -16t² + 10t + 6
When h = 0, -16t² + 10t + 6 = 0.
=> -8t² + 5t + 3 = 0
=> (-8t - 3)(t - 1) = 0
=> t = 1 or t = -3/8 (rejected as time cannot be negative)
Hence 1 second passed before the ball hits the ground.
Investors buy a studio apartment for $140,000. Of this amount, they have a down payment of
$42,000. Their down payment is what percent of the purchase price? What percent of the purchase
price would a $49,000 down payment be?
Their down payment is % of the purchase price.
Answers
Answer:
their down payment is 30%
Step-by-step explanation:
Answer:
Step-by-step explanation:
if the price of the apartment is 140,000 dollars
lets find out how much is 1%
140,000/100=1400
42,000/1400=30
42,000 is 30% of the apt price
49,000/1400=35
49,000 is 35% of the apt price
I need help pleas I need it please please please free 50 points
Answers
Answer:
answer is 0
Step-by-step explanation:
Answer:
its zero
Step-by-step explanation:
28 divided by 4 is 7
7 to the power of 2 is 49
49 divided by 7 is 7
7-7 is 0
In a class 3/4 of the boys like math, 1/2 like science, 1/4 of those who like science do not like math. How many boys like neither math nor science?
A. 1/4
B. 1/6
C. 1/2
D. 1/8
Answers
D.1/8
help asaap dont use me for points please
Answers
Answer:
-1.5
Step-by-step explanation:
You were on the free points page
The sum of two numbers is 14 one number is two less than three times the other. find the numbers
Answers
Answer:
The two numbers are 4 and 10
Step-by-step explanation:
give me a thanks bro
Please help soon! Thanks! Solve for x
Answers
Answer:
[tex]x=30^{\circ}[/tex]
Step-by-step explanation:
Looking at [tex]\triangle LMN[/tex]:
[tex]\angle NML = 180 - (90+45)[/tex] (angle sum of triangle is [tex]180^{\circ}[/tex])
[tex]=45^{\circ}[/tex]
Looking at [tex]\triangle KNM[/tex]:
[tex]\angle KNM = 180-105[/tex] (angle of straight is [tex]180^{\circ}[/tex])
[tex]=75^{\circ}[/tex]
[tex]\angle KNM + \angle NKM + \angle KMN = 180[/tex] (angle sum of triangle is [tex]180^{\circ[/tex])
[tex]75+2x+45 = 180[/tex]
[tex]2x+120 = 180[/tex]
[tex]2x=60[/tex]
[tex]x=30^{\circ}[/tex]
Hope this helps :)
ILL GIVE YOU BRAINLIEST IF YOU HELP ME
Answers
Answer:
y = (1/2) x - 2
Step-by-step explanation:
Let us consider the points (- 2, - 3) & (0, - 2)
Equation of line in two point form is given as:
[y-(-3)]/[-3-(-2)] = [x - (-2)]/[-2 - 0]
(y + 3)/(-3 +2) = (x + 2)/ (-2)
(y + 3)/(-1) = (x + 2)/(-2)
(y + 3)/(1) = (x + 2)/(2)
2(y + 3) = (x + 2)
2y + 6 = x + 2
2y = x + 2 - 6
2y = x - 4
y = (1/2) x - 2
PROCEED IN THE SAME WAY TO FIND OUT THE REMAINING FUNCTIONS.
Which two integers are 7 units away from the number 0 an a number line ?
1. -2 and 12
2. -2and 2
3. -2and 7
4. -7 and 7
Answers ASAP!!!!!
Answers
Question:
Which two integers are 7 units away from the number 0 an a number line ?
Answer:
-7 and 7
solve for X enter your answer in the Box
Answers
Answer:
x = 10
Step-by-step explanation:
Since the angles are equal I believe you can just set the ratios equal, cross multiply and solve
A ps4 uses uses 8.8 watts when on stand by mode. If electricty in your area costs 0.10$ kwh, how much would this cost?
Answers
Answer0.88:
Step-by-step explanation: because for every watt 10 cents or .10 is being used so since there is 8.8 watts it would be a total of 0.88 in your area
Function or Non-Function
Answers
Answer:
2 is not a function.
3 is a function
Step-by-step explanation:
one x value should each have a line leading off it. there are 2 y values for one x values in question 2 so its not a function
What is the area of the trapezoid.
Answers
Answer:
60
Step-by-step explanation:
base times height
1. An iPhone is on sale for $780. It originally cost $1000.00. What is the percent of change?
Answers
Answer:
your answer is going to be 220.
Ryan's dog weighs 50 pounds, and Mark's dog weighs p pounds. Which expression shows their combined weight? A. 50 × p B. 50 + p C. 50 ÷ p D. 50 - p
Answers
Answer:
B, 50 + p.
Step-by-step explanation:
To combine their weight, you would add them together. B is the only answer that uses addition.
what’s the answer to this ?
Answers
Answer:
the answer should be [tex]-20.2m - 11.8[/tex]
Step-by-step explanation:
Write the mixed number as a percent.
4 7/500
Answers
Answer:
4 7/500 as a percent is 401.4%
The mixed fraction [tex]4\frac{7}{500}[/tex] can be represent as 401%.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Fraction : 4 7/500
Now, writing the fraction in normal fraction form
= 4 7/500
= 2007/500
Now, to convert into percent
= 2007/ 500 x 100
= 2007/ 5
= 401%
Learn more about fraction here:
https://brainly.com/question/10354322
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Fewer young people are driving. In , of people under years old who were eligible had a driver's license. Bloomberg reported that percentage had dropped to in . Suppose these results are based on a random sample of people under years old who were eligible to have a driver's license in and again in . a. At confidence, what is the margin of error and the interval estimate of the number of eligible people under years old who had a driver's license in ?
Answers
The margin of error is 0.027 and the interval estimate at 95% confidence interval is 0.612 to 0.666
How to calculate the margin of error and the interval estimateFrom the question, we have the following parameters that can be used in our computation:
Proportion, p = 63.9%
Sample size, n = 1200
The margin of error can be calculated using:
E = z * √((p * (1 - p))/n)
Where
z = 1.96 i.e. z-score at 95% CI
Substitute the known values in the above equation, so, we have the following representation
E = 1.96 * √((0.639 * (1 - 0.639))/1200)
Evaluate
E = 0.027
The interval estimate is calculated as
I = p ± E
So, we have
I = 0.639 ± 0.027
Evaluate
I = 0.612 to 0.666
Hence, the interval estimate is 0.612 to 0.666
Read more about confidence interval at
https://brainly.com/question/15712887
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Question
Fewer young people are driving. In 1995, 63.9% of people under 20 years old who were eligible had a driver’s license. Bloomberg reported that percentage had dropped to 41.7% in 2016. Suppose these results are based on a random sample of 1200 people under 20 years old who were eligible to have a driver’s license in 1995 and again in 2016.
At 95% confidence, what is the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver’s license in 1995?
Helpppppppppppp!!!!!!!!!
Answers
Answer: The answer is D. 1/16
Step-by-step explanation: If you think about it, 2 to the 4th power is 16. But in this situation, you have a negative exponent. To solve an exponent situation with a negative situation, put a 1 as the numerator and put the answer of the expression but with the exponent's positive value as the denominator. Hope this helps :D
My head is hurting can you help me
It’s 16 points
Answers
Answer:
-6, -4
Step-by-step explanation:
If you flip the shape over the Y axis you can see