1. A signal tower has two lights that are 30 feet apart from each other, one directly above the other. From
a boat, the angle of elevation of the lower light is 14 degrees, and the angle of elevation yo the upper
light is measured to be 32 degrees.
a) Find to the nearest foot the distance from the boat to the lower light.
b) The boat and the foot of the tower are in the same horizontal plane. Find to the nearest foot the
distance from the boat to the foot of the tower.
Answers
Solution :
It is given that the distance between the two lights is 30 feet.
The angle of elevation of the upper light from the boat, ∠ ABP = 32 degree
The angle of elevation of the lower light from the boat, ∠ ABQ = 14 degree
∴ ∠ PBQ = ∠ ABP - ∠ ABQ
= 32 - 14
= 18 degree
In triangle PAB
∠ PAB = 180 - (90 + 32)
= 58 degree
Similarly in triangle AQB
∠ AQB = 180 - (90 + 14)
= 76 degree
Now considering triangle PBQ and applying the sine theorem,
[tex]$\frac{PQ}{\sin 18}=\frac{BQ}{\sin 58}$[/tex]
we know PQ = 30 feet
∴ [tex]$BQ =\frac{\sin 58}{\sin 18} \times 30$[/tex]
= 82.33 feet
Again taking the right triangle ABQ and applying sine theorem,
[tex]$\frac{BQ}{\sin 90}=\frac{AB}{\sin 76}$[/tex]
[tex]$\frac{82.33}{\sin 90}=\frac{AB}{\sin 76}$[/tex]
∴ [tex]$AB = 82.33 \times \sin 76$[/tex]
= 79.88 ft
= 80 feet
Related Questions
solve the following equation
x/3 +4 =7
Answers
Answer:
Sorry if im wrong..
Step-by-step explanation:
7 = (7 x)/3 + 4 = 21 x + 4 = 7
-4 -4
X/3=3
3.3 3.3
X=9
a woman sold an article for 400.00and made a profit of 25%,Find ty cost price and profit
Answers
Answer:
$100 profit, $300 cost
Step-by-step explanation:
So 25% of $400 is $100, now we know she made $100 on the article
and the other $300 was the amount used to make the article i'm asuming
A woman sold an article for 400.00
made a profit of 25%
Cost price and profit is $100 profit, $300 cost.
What are the 4 types of profit?There are four levels of profit or profit margins: gross profit, operating profit, pre-tax profit, and net profit.
These are reflected on a company's income statement in the following sequence: A company takes in sales revenue, then pays direct costs of the product of service.
What is profit and example?Profit is a term that often describes the financial gain a business receives when revenue surpasses costs and expenses. For example, a child at a lemonade stand spends one quarter to create one cup of lemonade. She then sells the drink for $2. Her profit on the cup of lemonade amounts to $1.75.
To learn more about Profit, refer
https://brainly.com/question/12225249
#SPJ2
Which of these strategies would eliminate a variable in the system of equations?
10x + 4y = -2
52 - 2y = 2
Choose all answers that apply:
A
1
Multiply the top equation by
2
then add the equations.
Add the equations.
Multiply the bottom equation by 2, then subtract the bottom equation from the top equation.
Answers
BRAINLIEST ANSWER (70 points)
Solve for x
Answers
Answer:
x = 22
Step-by-step explanation:
6x + 48 = 180
6x = 132
X = 22
Number 6 please help 10 points
Answers
Answer: The graph would have 4 bars
Step-by-step explanation: The graph would have 4 bars because there are 4 numbers
The shapes of the horizontal cross-sections of the cylinder below are not all
congruent
A. True
B. False
Answers
If f(x) equals 4^x- 8 and g(x) equals 5times + 6, find (f-g)(x)
Answers
Step by step exploration
(f-g)(x)= 4^x- 8-5x- 6= 4^x-5x-14 so C
ILL BRAINLIEST YOU IF YOU GET IT RIGHT
Which diagram shows a pair of angle measure that proves lines c and d are parallel?
Answers
Answer:
C
Step-by-step explanation:
At first glance, it seems like all the answers work. But some careful thinking allows us to find the correct answer.
For this question, we will be using the process of elimination.
First, we can eliminate D, because it does not provide any angles on line d, so we cannot prove that line c is parallel to line d.
Second, we can eliminate A. It seems that the 2 angles makes it so that lines c and d must be parallel, however, that is only true if lines a and b are parallel. Since we don't know whether or not lines a and b are parallel, we cannot prove that lines c and d are parallel, so we can eliminate this choice.
Third, we can eliminate B. Like the diagram in A, this diagram can only prove lines c and d are parallel if lines a and b are parallel, and since we don't know whether or not lines a and b are parallel, we cannot prove tat lines c and d are parallel, so we can eliminate this choice.
We are left with C, so the answer must be C.
Of course, just to make sure, we will also check diagram C. Because the 2 angles provided in the diagram are on line a and none are on line b, we do not need line a to be related to line b in any way, as such we can pretend that line b does not exist in this diagram. We can then see that lines c and d must be parallel for this diagram, or else the angles would not work, so C is correct.
Two angles whose sum is 180° are called supplementary angles. The correct option is C.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
When two parallel lines are cut by a transverse. The angles formed on the exterior of the parallel lines are known as the Exterior Angle.
Now, For two lines two be parallel in the given diagram the measure of the angle the exterior angle on the same side of the transverse should be supplementary to each other.
The diagram shows a pair of angle measure that proves lines c and d are parallel in option c. This is because lines c and d are parallel and a is transversal to the two lines. And the measure of the exterior angles formed on the same side of the transversal is supplementary.
Hence, the correct option is C.
Learn more about Supplementary angle here:
https://brainly.com/question/2882938
#SPJ2
please help
1. find 15% of 120
2. what percent of 72 is 68.4
3. 12.5 is 8% of what number?
4. 48 is 40% of what number
5. what number is 62.5% of 195
Answers
1% = 120 ÷ 100 = 1.2
15% = 1.2 × 15 = 18
So, 15% of 120 is 18
For question 2:
68.4 ÷ 72 = 0.95
0.95 × 100 = 95%
So, the percentage is 95%
For question 3,
1% = 12.5 ÷ 8 = 1.5625
100% = 1.5625 × 100 = 156.25
So, 8% of 12.5 is 156.25.
For question 4,
1% = 48 ÷ 40 = 1.2
100% = 1.2 × 100 = 120
So, 40% of 48 is 120.
For question 5,
1% = 195 ÷ 100 = 1.95
62.5% = 1.95 × 62.5 = 121.875
So, 62.5% of 195 is 121.875
Answer:
1. 18 3. 52 5. 95%
Step-by-step explanation:
1. 120 x 0.15= 18.00 (15% of 120 is 18)
3. 84 x 0.03= 2.52
5. 72• x / 72 = 68.4/ 72
x=0.95 ⇒ 95%
Can you help me. .....................
Answers
Answer:
2
Step-by-step explanation:
In rectangle ABCD the slope of AB is 1/2 what is the slope of CD
Answers
Answer:
there is no picture of what i need to solve
Step-by-step explanation:
7. What is the image of p for a dilation with center (0,0) and a scale factor of 2.5?
A (-2.5, 5)
B (2.5, -5)
C (2, 2.5)
D (-5, -2.5)
Answers
Answer:
A (-2.5, 5) Might Not Be Right
Step-by-step explanation:
You have 4 hours, and 50 questions. If you have the same amount of time per question, how long will 1 question take?
Answers
Plz give brainliest
Triangle JKL with vertices J(1,-1), K(2,3), and L(3,-2) in the line x=4 ANSWER RIGHT NOW BEEN WAITING AN HOUR NOW
Answers
Answer:
hahhahahqhqhqhhajajahahahahahwhwhwhwhwh
Thank you so much :)
Answers
Answer:
b
Step-by-step explanation:
Find the 1st 4 iterations if f(o)= -2, f(n)= 3f(n-1)-2n
Answers
Answer:
Step-by-step explanation:
f(0) = -2
f(1) = 3*(f(1 - 1)) - 2*1
f(1) = 3(-2) - 2
f(1) = - 6 - 2
f(1) = - 8
f(2) = 3*(f(1)) - 2*2
f(2) = 3*(-8) - 4
f(2) = -24 - 4
f(2) = - 28
f(3) = 3*(f(2)) - 2*3
f(3) = 3*-28 - 6
f(3) = -84-6
f(3) = - 90
f(4) = 3*f(3) - 2 * 4
f(4) = 3*-90 - 8
f(4) = -270 - 8
f(4) = -278
SYTEM OF INEQUALITIES , 65 points.
HELP
Answers
Answer:
[tex]2x+3y\geq 60\\x>10[/tex]
Step-by-step explanation:
We know that she will be selling bracelets for $2 each and earrings for $3 each. That means we will have 2x+3y, where x is the number of bracelets she sells and y is the number of earrings she sells. Then we will have [tex]\geq 60[/tex] because she wants to sell at least $60 worth of earrings and bracelets. That means the amount she makes from bracelets and earrings combined has to equal 60 or more, thus we use the greater than or equal to sign.
Now we have [tex]x>10[/tex], where x is still the number of bracelets sold. She said she will sell more than 10, which means we will just have [tex]>10[/tex]. If she said she wanted to sell at least 10, then it would be [tex]\geq10[/tex].
Therefore the system of inequalities is:
[tex]2x+3y\geq60\\x>10[/tex]
Hope this helps!
????????????????? I NEED HELP WITH THIS WILL GIVE BRAINLIEST
Answers
Answer:
#3 is 40
#4 is 90
Step-by-step explanation:
Who is the volume of a sphere that has the radius of 3 inches
Answers
Answer:
113.1
Step-by-step explanation:
i just did the math
Answer:
113.1 is the answer
I just multiplied
Melissa is saving money to buy a game. So far she has saved $20, which is four-fifths of the total cost of the game. How much does the game cost?
Answers
Answer:
25
Step-by-step explanation:
5 10 15 20 25
Answer:
25 dollars
Step-by-step explanation:
20 divided by 4 equals 5 then times that by 5 equals 25 then thats the total and ur answer is 25
The circumference of a circle is 2\piπ m. Find its radius, in meters.
NO FILES TYPE THE ANSWER PLZ
Answers
Answer: r=C2π=22·π≈0.31831
Hope this helps!
What is the value of X?
Answers
Answer:
23
Step-by-step explanation:
83+3x+90+x+95= 360
4x= 360-83-90-95
4x= 92
x= 23
hey could someone help me with this. i’ll mark u brainiest if u don’t leave a link.
Answers
Answer:
10,000
Step-by-step explanation:
10 to the power of 4 is equal to 10x10x10x10 which is 10,000! I hope this helps
Answer:
the answer will be 10000!
Step-by-step explanation:
10 x 10 x 10 x 10 = 10000
or...
10 x 10 = 100
100 x 100 = 10000
or...
jusr simply add 4 zero to 1!
Evaluate x^2, when x is 1/2
Answers
Answer:
1/4
Step-by-step explanation:
1/2*1/2
1. You start a biology experiment with 4,500 cells. The cells are continuously growing and 2 minutes later
there are about 22583 cells. What is the rate of growth per minute?
Answers
Answer:
80.65% per minute
Step-by-step explanation:
For continous growth :
A = Pe^rt
A = amount after time, t
P = initial amount
r = growth rate
22583 = 4500 * e^r*2
22583 = 4500 * e^2r
22583 / 4500 = e^2r
5.0184444 = e^2r
Take the In of both sides
1.61312 = 2r
r = 1.61312 ÷ 2
r = 0.80656
0.80656 * 100% = 80.65%
Kyle is a satellite radio sales representative. He receives 7% commission on all sales. If
the total sales for the year were $345,000, what would his commission be?
Answers
Answer:
24,150
Step-by-step explanation:
7% of 345,000 = 24,150
A coffee shop sells 40 regular coffees out of every 120 coffees they sell. Predict how many regular coffees the shop would sell if they sold 960 coffees.
Answers
Answer:
320
Step-by-step explanation:
960 ÷ 120 = 8
40 × 8 = 320
Please answer my math question
Answers
x=2 or x=-8 are the answers to the questio.
Which is a true statement based on the dot plots below?
.
++
10 20 30 40 50 60
Set A
10 20 30 40 50 60
Set B
O Set A has the greater mean.
O Set A has the lesser range.
O Set B as the greater median
O Set B is less symmetric than Set A
Answers
PLEASE HELP! (Q~Q)
Please show work...
Answers
Answer:
cross multiply 2 to 15 then divide whatever the outcome is by 0.5
Step-by-step explanation:
when 1 * 0.5 whole answer will be outcome