A lifeguard is in an observation chair and spots a person who needs help. The angle of depression to the person is 22°. The eye level of the lifeguard is 10 feet above the ground. What is the horizontal distance between the lifeguard and the person? Round to the nearest foot.
Answers
Answer:
The horizontal distance between the lifeguard and the person is approximately 24.751 feet.
Step-by-step explanation:
At first we include a geometrical representation of the statement, which is shown in the image attached below. We can determine the horizontal distance between the lifeguard and the person by means of the following trigonometrical relationship:
[tex]\tan \theta = \frac{OL}{OP}[/tex] (1)
Where:
[tex]\theta[/tex] - Angle of depression to the person, measured in sexagesimal degrees.
[tex]OL[/tex] - Height of the lifeguard above the ground, measured in feet.
[tex]OP[/tex] - Horizontal distance between the lifeguard and the person, measured in feet.
If we know that [tex]OL = 10\,ft[/tex] and [tex]\theta = 22^{\circ}[/tex], then the horizontal distance between the lifeguard and the person is:
[tex]OP = \frac{OL}{\tan \theta}[/tex]
[tex]OP = \frac{10\,ft}{\tan 22^{\circ}}[/tex]
[tex]OP \approx 24.751\,ft[/tex]
The horizontal distance between the lifeguard and the person is approximately 24.751 feet.
Related Questions
The high for yesterday was 90°F, today the high is 78°F. What is the percent decrease in the
temperatures?
Answers
Answer:
The temperature from yesterday to today decreased by 12 degrees fahrenheit.
Step-by-step explanation:
Ummm... it's true :)
The temperature at 6:00 pm was 15 degrees Celcius. The temperature dropped 2 degrees Celcius per hour. What was the temperature at 4:00 am
Answers
Answer:
-5 Celsius
Step-by-step explanation:
You find the hours between which is 10 then you multiply 10 to 2 and then subtract
Help will get brainliest
Answers
for question 3 answer is 53 7/8 feet
The subtotal for a TV was $1,029.99. What does that mean?
Answers
What is the area of △MNP?
A. 40 m2
B. 60 m2
C. 68 m2
D. 127.5 m2
Answers
answer is B. 60 m2
Step-by-step explanation:
17²=15²+MP²
289=225+MP²
289-225=64
So... MP²=64.... MP=8
8×15= 120
120÷2=60
-7(x + 9) = 9(x - 5) - 14x Solve for x. SHOW WORK.
Answers
Answer:
x=-9
Step-by-step explanation:
STEP 1: Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.
[tex]9(x-5)-14x=-7(x+9)[/tex]
STEP 2: Simplify 9(x−5)−14x.
[tex]-5x-45=-7(x+9)[/tex]
STEP 3: Simplify −7(x+9).
[tex]-5x-45=-7x-63[/tex]
STEP 4: Move all terms containing x to the left side of the equation.
[tex]2x-45=-63[/tex]
STEP 5: Move all terms not containing x to the right side of the equation.
[tex]2x=-18[/tex]
STEP 6: Divide each term by 2 and simplify.
[tex]x=-9[/tex]
Answer:
x= -9
explanation in the pic above
hope it helps.
what is the reciprocal of 2 1/2
Answers
Answer:
2/5
0.4
Step-by-step explanation:
Answer:
0.4
Step-by-step explanation:
Adam currently runs about 40 miles per week, and he wants to increase his weekly mileage by 10%. How many miles will Adam run per week?
Answers
it would be 50miles i think or it would be 44
Last month you spend $30 on clothing this month you spent 160% of what you spent last minute set up a proportion to model this situation how much did you spend this month
Answers
Answer: See explanation
Step-by-step explanation:
From the question, we are informed that last month $30 was spent on clothing and that this month, 160% of what was spent last month.
The equation to to model this situation will be:
= 160% × $30
= 160/100 × $30
= 1.6 × $30
= $48
That means $48 will be spent this month.
Write an inequality that has no solution when
solved-- meaning your answer needs to have a
variable in it.
Answers
Answer:
3x > 3x+2
Step-by-step explanation:
inequality with no solutions will give you something that is never true like
3 > 5 so for example you can have
3x > 3x+2
can someone help me out i don’t understand
Answers
Answer:
-4
Step-by-step explanation:
180-80=100
100-64=36
36-44=-8
-8/2=-4
What value of x satisfies the equation x/4 + x/2 =9
Answers
"12" is the correct value of "x" which satisfies the given equation.
The given equation is:
→ [tex]\frac{x}{4} +\frac{x}{2} =9[/tex]
By taking L.C.M, we get
→ [tex]\frac{x+2x}{4}= 9[/tex]
→ [tex]\frac{3x}{4} =9[/tex]
By applying cross-multiplication, we get
→ [tex]3x=36[/tex]
→ [tex]x = \frac{36}{3}[/tex]
→ [tex]= 12[/tex]
Thus the above is the right answer.
Learn more about equation here:
https://brainly.com/question/1054939
Solve the inequality: 1 < x-2<5
O [3,7]
O (3,7)
O [7,3]
O (7,3)
Answers
Answer:
3,7
Step-by-step explanation:
Answer:
(3, 7 )
Step-by-step explanation:
Given
1 < x - 2 < 5 ← add 2 to each interval
3 < x < 7
Since x cannot equal 3 or 7 then use parenthesis for limits, that is
solution is (3, 7)
The average temperature in May is
63.4º.
The average temperature in January is
42.34º.
About how much warmer is it in May
than in January?
Answers
HELPPP PLZZZZZ I DONT KNOWW HOW TO DO THSSS
Answers
Answer:
Join Zoom Meeting
Meeting ID: 580 387 3474
Passcode: 1234
Answer:
Step-by-step explanation:
y=-x-4
-2( x - 3 ) = 8x -3( 5 + x )
find the value of x
Answers
Answer:
0.45
Step-by-step explanation:
what is the value of angle k
Answers
Answer:∠k = 121°
Step-by-step
Exterior Angle Theorem:
The measure of an exterior angle is equal to the sum of the two remote interior angles.
Add 31° and 90° to get ∠K
An unbalanced force causes a change in _________________ or _________________________.
50 POINTS!
A balanced force ____________________________________. It has a net force of _______________.
The UNIT for force is the _______________________________. It is abbreviated ________.
Answers
Answer:
What?
Step-by-step explanation:
What is the value of y in the equation 2(4y − 1) = 6? (4 points) a 0 b 1 c 6 d 8
Answers
Answer:
B; 1
Step-by-step explanation:
divide both sides of the equation by 2
4y-1=3
move the constant to the right
4y=3+1
calculate (add the numbers)
4y+4
divide both sides by 4
y=1
Answer:
b
Step-by-step explanation:
need help asap please!!
Answers
Answer:
Step-by-step explanation:
Your worth it love u
Eight bottles of soda and four bags of chips cost $16. Six bottles of soda and 7 bags of chips cost $14. How much does a bottle of soda cost? How much does a bag of chips cost?
Answers
Answer: soda 1.75 dollars and chips is 0.50 dollars
Step-by-step explanation:you have to work out the question like a simultaneous equation so key s=soda and c=chips
8s+4c=16
6s+7c=14 make chips equal
56s+28c=112
24s+28c=56 Take the equations away
32s=56
S=56\32
S=7/4
S=1.75 sub that answer in the first equation
8*1.75=14
14+4c=16
4c=2
C=0.5
find the slope of the line√3y-x-2√x
Answers
Please help me with this problem
Answers
Answer:
The angle of EDA is 45 and I believe BE is 19.
Step-by-step explanation:
Solve the inequality. Graph the solutions.
Answers
Answer:
d
Step-by-step explanation:
i took the test
Answer:
C. x < -5 or x > 5
Step-by-step explanation:
A local school donated canned goods to help the community. Cans were packed into boxes each weighing 16.4 pounds. The volunteers packed 9 boxes. How many total pounds of food did they collect? A. 97.6 B. 147.6 C. 976 D. 1,476
Answers
Answer:
147.6 pounds of foodStep-by-step explanation:
Each box weighed 16.4pounds, if the volunteers packed 9 boxes, we need to calculate the total pounds of food collected. Using the equality postulate;
1 box = 16.4 pounds
9 boxes = x pounds of food
Cross multiply;
1 * x = 9 * 16.4
x = 147.6 pounds of food
Hence the volunteers collected 147.6 total pounds of food
HELP PLEASE! :) Lilith is remodeling her bathroom and needs an $8,700 loan to pay for the cost of the remodel. Which loan option will have Lilith pay the most amount in interest? 30-month loan with a 5.75% interest rate compounded annually 30-month loan with a 5.75% annual simple interest rate 24-month loan with a 6.25% interest rate compounded annually 24-month loan with a 6.25% annual simple interest rate
Answers
Answer:
Which loan option will have Lilith pay the most amount in interest
loan with a 5.75% annual simple interest rate 24-month loan with a 6.25% interest rate
Interest 3,750
Final payment 33,750
Step-by-step explanation:
1.-Interes rate compouned
Loan 30,000
% 5.75%
Time( Years) 2.50
Interest 4,500
Final payment 34,500
2.-Simple interest
Loan 30,000
% 5.75%
Time( Years) 2.50
Interest 4,313
Final payment 34,313
3.-Simple interest
Loan 30,000
% 6.25%
Time( Years) 2.00
Interest 3,750
Final payment 33,750
4.-Interes rate compouned
Loan 30,000
% 6.25%
Time( Years) 2.00
Interest 3,867
Final payment 33,867
The loan option that will cause Lilith to pay the most interest is a 30-month loan with a 5.75% interest rate compounded annually.
A simple interest is a kind of interest that is charged only on the principal while a compound interest is a kind of interest that is charged both on the principal and the interest.
The loan option that will cause Lilith to pay the most interest is a 30-month loan with a 5.75% interest rate compounded annually.
Learn more about compound interest: https://brainly.com/question/25857212
What is the slope of the line through (−1,−7) and (3,9)?
Answers
Answer:
The slope is 4.
Step-by-step explanation:
Point slope form is y-y1 over x-x1. I put the coordinates in like this.
9-(-7) over 3-(-1) so thats 9+7 over 3+1. 16 over 4 is 4.
Answer:
The answer is 2
Step-by-step explanation:
The following chart shows the number of rows in an auditorium and the total number of seats. What equation defines the number of seats with respect to the number of rows?
Answers
Answer:
S=30R+45
Step-by-step explanation:
3045/100=30R +45
So the other ones will be the same if this one is the answer. If you want you can check with the other ones. It's really easy if you get to understand it.
Answer:I am not sure
Step-by-step explanation:
Students at Mendel Middle School are planning a fair for their school's fundraiser. Liam volunteers to help plan the event. The first month, he volunteered for x hours. The next month, he volunteered for 1 2/3 times as many hours as he had the first month. If he volunteered for a total of 40 hours, how many hours did he volunteer during the first month? Write an equation to represent the situation and solve.
Answers
Answer:
15 hours
Step-by-step explanation:
[tex]x[/tex] is the number of hours that Liam volunteered in the first month
The next month he volunteered [tex]1\dfrac{2}{3}[/tex] times the time he volunteered the first month.
Total time he volunteered in the two months is 40 hours so
[tex]x+1\dfrac{2}{3}x=40\\\Rightarrow x+\dfrac{5}{3}x=40\\\Rightarrow \dfrac{3x+5x}{3}=40\\\Rightarrow x=\dfrac{40\times 3}{8}\\\Rightarrow x=15[/tex]
Time he volunteered in the first month is 15 hours.
An individual can win a prize by drawing the highest numbered card out of five cards. After each draw, the card is replaced and the cards are shuffled for another chance. If the prize is not won, the card is again replaced and mixed in with the other cards. If a prize is won, the highest card is replaced and the five cards are shuffled for a new game. If an individual makes seven draws, what is the probability the individual will win a prize exactly two times?
A. 2 factorial over 7 factorial
B. 7 choose 2 times 0.2 squared times 0.8 to the fifth power
C. 0.2 squared over 0.8 to the fifth power
D. 2(0.2)(0.8)
E. (0.2)2(0.8)5
Answers
Answer:
B
Step-by-step explanation: