You see a hiker sitting on a bench taking a water break at the top of a hill at a 40° angle of elevation. Your eye level is 5 feet off the ground and you are standing 100 feet from the base of the hillAt what altitude is the hiker sitting on the bench?
Answers
Answer:
89
Step-by-step explanation:
Draw a right triangle, put the angle of elevation as 40 degrees and the feet for the base of your triangle (standing 100 feet from the base of the hill) as 100ft. According to SOH CAH TOA, we will be using tan, where you will get:
tan(40)=x/100
x=100tan(40)=83.9
Add 5 feet, which was your eyes off the ground, and it will be 83.9+5=89
Final Answer: 89
The altitude of the hiker sitting on the bench of the hill is 89 feet.
What is trigonometry?Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.
For the given situation,
The angle of elevation = 40°
Distance from base of the hill = 100 feet
Distance from the ground to the eye level = 5 feet
The diagram below shows the right angled triangle.
Let the altitude from the eye sight to the bench be x.
Total altitude = x + 5
The altitude of the hiker can be found by using trigonometric ratio,
[tex]tan\theta= \frac{opposite}{adjacent}[/tex]
⇒ [tex]tan 40=\frac{x}{100}[/tex]
⇒ [tex]0.8390=\frac{x}{100}[/tex]
⇒ [tex]x=83.90[/tex]
Total height = [tex]x+5[/tex]
⇒ [tex]83.90+5[/tex]
⇒ [tex]88.90[/tex] ≈ [tex]89[/tex]
Hence we can conclude that the altitude of the hiker sitting on the bench of the hill is 89 feet.
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Related Questions
HELP PLEASE DUE IN 4 MINUTES
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Step-by-step explanation:
If two angles are vertical, the sum of their measures is equal to the measure of a right angle true or false?
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Step-by-step explanation:
False,
Vertical angles isn't always complementary l
Answer:
true
Step-by-step explanation:
If two angles are congruent, their measures are equal.
5 + (1/7)b = -2
what is b?
Answers
Answer: b=-1
Step-by-step explanation:
[tex]5+\frac{1}{7}b=-2\\\\5+\frac{1}{7}b=-2\\\\\frac{1}{7}b=-7\\\\b=-1[/tex]
help please i’ll give extra points
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Answer:
P would be reflected into quadrant 4.
Step-by-step explanation:
Answer:
Quadrant 4
Step-by-step explanation:
The quadrant under P is quadrant 4. Imagine putting a mirror on the x-axis, where would P be? It would be on the fourth quadrant, the quadrant underneath P.
Have a nice day!
daniel has x coins, paula has 2 time as many coins as Daniel
Answers
Answer:
Paula = 2x coins
Step-by-step explanation: We don't know how many x is, but we know that whatever x is, Paula is going to have double that number of coins. Turn this explanation into an equation... 2x...
Does anyone know the answer to this?
Answers
It help u
1. The diameter of a circle is 8. what is the radius?
Answers
Answer:
Radius = 4
Step-by-step explanation:
r = d/2
r = 8/2
r = 4
Answer:
4
Step-by-step explanation:
The diameter of a circle is the length of a straight line from two opposite points on the circle. The radius is the length of a straight line from the middle to a point on the circle. This means that the diameter must be double the radius. So to find the radius, divide the diameter by 2. Since 8/2=4, the radius is 4.
Leilani wants to make 8 placemats. For each placemat she needs 18 in of fabric. How many yards of fabric will she need for
the 8 placemats?
Answers
Answer:
144 yarns of fabric
Step-by-step explanation:
If 8 placemat =18 fabrics
then 8 p placemats=8x18
=144
Leilani wants to make 8 placemats. For each placemat she needs 18 in of fabric. Leilani will need 4 yards of fabric to make the 8 placemats.
To determine the amount of fabric Leilani will need for 8 placemats, we need to convert the given length from inches to yards.
Given:
Length of fabric needed for one placemat = 18 inches
To convert inches to yards, we divide the length in inches by 36 (since there are 36 inches in a yard).
18 inches / 36 = 0.5 yards
Therefore, for one placemat, Leilani will need 0.5 yards of fabric.
To find the total amount of fabric needed for 8 placemats, we multiply the fabric requirement for one placemat by 8:
0.5 yards/placemat * 8 placemats = 4 yards
Leilani will need 4 yards of fabric to make the 8 placemats.
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Full Question.
Leilani wants to make 8 placemats. For each placemat she needs 18 in of fabric. How many yards of fabric will she need for the 8 placemats?
( No graph Needed)
A bag contains: • 2 white marbles • 3 brown marbles • 4 purple marbles • 6 orange marbles A marble will be drawn from the bag and replaced 75 times. What is a reasonable prediction for the number of times a brown or purple marble will be drawn?
Answers
Answer:
45
Step-by-step explanation:
There are 14 total marbles. The probability of drawing a yellow marble on the first draw is 3/14. Given replacement, the probability on the second draw is the same as on the first draw, so the probability of black marble on the second draw is 6/14. The probability of drawing first a yellow marble then a black marble is 3/14 * 6/14 = 18/196.
Answer:
35
Step-by-step explanation:
sorry, i dont have an explanation for this i just guessed and it was right, here u go :)
I don’t know what to do
Answers
Answer:
i think it would be the first one i am not 100% sure just a gues
Step-by-step explanation:
What is the probability that a data value in a normal distribution is between a
z-score of -0.37 and a z-score of 1.22? Round your answer to the nearest
tenth of a percent.
A. 54.3%
B. 52.3%
C. 51.3%
D. 53.3%
Answers
Answer:
53.3%
Step-by-step explanation:
It's the correct answer that's why
can somebody help me with math I have 3 more questions OWO:
If Jeff drives 200 miles per hour in his race car, and this relationship is graphed, which ordered pair would not be on the graph?
1. (2, 400)
2. (0, 0)
3. (8, 1,600)
4. (5, 1,200)
please don’t steal all my points UwU :( :’)
Answers
The ordered pair would not be on the graph is (5, 1200)
The correct option is (4).
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
If Jeff drives 200 miles per hour in his race car.
So, if we denote the distance by y and time by x then relation is
y = 200x
For x = 0
y=0
and, x= 2
y= 400
and, x= 8
y= 1600
and, x= 5
y = 1000
Hence, the point not on the graph is (5, 1200)
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WILL MARK BRAINLIST JUST HELP ME
What is the volume of the triangular prism?
A) 15 cm3
B) 18 cm3
C) 21 cm3
D) 24 cm3
Answers
Answer:
A
Step-by-step explanation:
Is the ratios 2.5 : 8 and 7.5 : 24 are they equivalent?
Answers
Answer:
Yes, they are equivalent.
Step-by-step explanation:
To get from 2.5 : 8 to 7.5 : 24, you have to multiply by both sides by 3.
So they are equivalent.
HELPPPPPPPPP MATH PLEASE
Answers
Answer: 14
Step-by-step explanation:
Answer:
12 units^2
Step-by-step explanation:
The triangle on the left has an area of 2, the square has an area of 4 and the triangle on the right has an area of 6.
Add these up to get 2+4+6 = 12
Each of the following hypothetical data sets represents some repeated weighings of a standard weight that is known to have a mass of 100 g. Assume that the readings are a random sample from a population that follows the normal curve. Perform a t test to see whether the scale is properly calibrated, if possible. If impossible, explain why.
a. 100.02.99.98,100.03
b. 100.01
Answers
Answer:
b
Step-by-step explanation:
What number would make this problem many solutions?
Infinity many solutions :
10x+ ___ =2(5x+7)
2
5
7
14
17
20
Answers
Answer:
14
.........................
Answer:
14
Step-by-step explanation:
Distribute the right hand side of the equation to get 10x +14. To have infinitely many solutions, the left hand side would be the same so the answer is 14.
The costs of a pack of noodles, a can of soda and a pack of bread buns are 120 Pesos, 45 Pesos, and 50 Pesos respectively. Brayden wants to buy x packs of noodles, y cans of soda, and z packs of bread buns.
Answers
This equation models this situation where C is the total cost
A rectangular poster has an area of 38 square feet. It is 4 3/4 feet wide at its base. What is the height of the poster
Answers
Answer: The height is 8
Step-by-step explanation:
4.75 x 8 = 32
Triangle XYZ has vertices X(1, –1), Y(3, 4), and Z(5, –1). Nikko rotated the triangle 90° counterclockwise about the origin. What is the correct set of image points for triangle X’Y’Z’?
X’(1, 1), Y’(-4, 3), Z’(1, 5)
X’(1, 1), Y’(–3, –4), Z’(–1, –5)
X’(–1, 1), Y’(–3, –4), Z’(–5, 1)
X’(–1, –1),Y’(4, –3), Z’(–1, –5)
Answers
Answer:
When a figure is rotated counterclockwise about the origin, its original coordinates of point P (x,y) will now be positioned as P' (-y,x).
X (1,-1) --> X' (1,1)
Y (3,4) --> Y' (-4,3)
Z (5,-1) --> Z' (1,5)
The correct set of image points for triangle X'Y'Z' is X'(1,1), Y'(-4,3), and Z'(1,5).
Step-by-step explanation:
Triangle XYZ is rotated 90° counterclockwise, the new coordinate is X'(1, 1), Y'(-4, 4) and Z'(1, -5)
TransformationTransformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.
If a point A(x, y) is rotated 90° counterclockwise the new point is A'(-y, x).
Triangle XYZ is rotated 90° counterclockwise, the new coordinate is X'(1, 1), Y'(-4, 4) and Z'(1, -5)
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1. Quadrilateral ABCD has AB = x+3 and CD= 5x –7. What is the length of x
for which the quadrilateral is a parallelogram?
Answers
Answer:
x = 2.5
Step-by-step explanation:
since it's a parallelogram, AB = CD so:
x + 3 = 5x - 7
subtract x from each side of the equation:
3 = 4x - 7
add 7 to each side:
4x = 10
divide both sides by 4:
x = 2.5
x over 8 = 10?
i just need to solve for x
Answers
A triangle has side lengths of 11 cm and 6 cm. Which could be the value of the third side, 21 cm or 14 cm? Is it 14 or 21?
Answers
Answer:
14
Step-by-step explanation:
As long as two sides of a triangle added together are larger than the third side, it is an accurate triangle!
please help ll do anything just help me with this question on math:
Which of the following is not the same as positive 3?
1. 3 units to the left of 0 on a number line
2. the opposite of -3
3. +3
4. 3
what’s the awnser? 1,2,3, or 4
Answers
answer:
3 units to the left of 0 on a number line
step-by-step explanation:
your asking for the opposite of positive 3 which just means your looking for a negative 3 ( also written like this -3 )
and going left on a number line means going down on a number line so if your going into the negatives if you started at 0
here is a small number line to help me explain this better
<----|----|----|----|----|----|----|----|----|----|----|---->
-5 -4 -3 -2 -1 0 1 2 3 4 5
* ( the star is you and your starting off at the #0 )
<|-(-1)-(-1)-(-1)- = -3 ( taking 3 jumps to the left )
*
( and now the star is at -3 which was the number you needed )
i hope this helps you and if you need anything else then just tell me! :)
help me plz branniest to whoever is right
Answers
Answer:
x= -7, x=8
Step-by-step explanation:
factoring method..
f (x) = - x² + 12x - 20
= - x² + 10x + 2x - 20
= - x( x - 10 ) + 2( x - 10 )
= ( x - 10 ) ( -x + 2 )
=> x = 10, x = 2
A student answered 43 questions correctly in a 53 questions test. What
percent is that?
Round your answer to the nearest whole.
%
Answers
Answer: 81%
Step-by-step explanation: I think i'm right
A class of fourth graders decides to split into groups based on the first letter of their last names.then,they choose students from each group.what type of sampling is used?
A.Quota sampling
B.Volunteer sampling
C.Purposive sampling
D.Convenience sampling
Answers
Answer:
Volunteers sampling is correct answer
what is 2/5 x 5/6
i need the answer in 3 minutes
Answers
1/3
...............
.
...........
Answer:
1/3
Step-by-step explanation:
nine divided by n plus two
Answers
Answer:
whats n?
Step-by-step explanation:
im guessing 9/1=9+2=11 idek bc u didnt give n
help someone plz I'll give brainlest
Answers
Answer:
like with the whole page?? cause if so i got this KINDA
Step-by-step explanation:
the first one (2/9+2/9) = 4/9
the second one (1/4+2/4)=3/4
the third one (3/8+5/8)=1 whole or 8/8
i cant see the last one so ill skip to the bottom row
the first one (2/5-1/5)=1/5
(9/12-4/12)=5/12
(4/10-2/10)= 2/10
and ill give someone else a shot with the rest of the questions but yw
this is pretty simple but hit me up if you ever need more help
=D
Answer:
Section 1
Adding and Subtracting- just add/subtract (depending on what the question is asking you) the numerators (top number), don't do anything to the denominators (bottom numbers)
Step-by-step explanation:
Section 1
Adding and Subtracting- just add/subtract (depending on what the question is asking you) the numerators (top number), don't do anything to the denominators (bottom numbers)
Section 2
Make the denominators (bottom numbers) the same, then add or subtract the numerators. To make the denominators same, apply a common factor to the bottom number.
Section 3
Multiply the top numbers and bottom numbers to get the answer.
Section 4
Use KCF: Keep, Change and Flip. Keep the first fraction the same, then change the division sign to a multiplication and finally flip the last fraction, then multiply the two fractions.