An 18-foot ladder is leaning against the side of a building such that its base makes an angle of 65º with the ground. How far from the side of the building, b, should the base of the ladder be placed? Round to the nearest tenth of a foot.
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Hello!
This problem is about relating trigonometric values to an unknown side.
We are given an angle side, and we can determine that another angle made would be a 90 degree angle.
Meaning we could solve for the third unknown angle by knowing that the interior angles of a triangle add up to 180 degrees.
[tex]65+90+x+180[/tex]
[tex]x=180-90-65[/tex]
[tex]x=25[/tex]
After knowing this, we could use the law of sines, which states that the ratio of a side and the sin of its opposite angle are equal to any other ratio.
[tex]\frac{16}{sin(90)}=\frac{b}{sin(25)}[/tex]
[tex]b=16sin(25)[/tex]
Make sure to be in degrees when putting this in a calculator.
[tex]b=6.8[/tex]
Hope this helps!
Related Questions
PLEASE HELP the graph of the function f(x)=5/4sin(x)+1 is shown. what are the key features of this function? (look at photo)
Answers
Answer:
2.25 -0.25 increasing (-0.25,2.25)
Step-by-step explanation:
The minimum and maximum values are negative 1/4 and 9/4. In the interval of (0, π/2), the function is decreasing. And the range of the function will be [–1/4, 9/4].
What is a sinusoidal Function?It is a function that repeats itself in a particular time interval.
The equation is given as
y = A sin (ωx + Ф) + C
Where A is the amplitude, ω is the frequency, Ф is the phase difference, and C is the constant.
The function is given below.
f(x) = (5/4) sin(x) + 1
Compare the function with standard equation.
A = 5 / 4
ω = 1
Ф = 0
C = 1
Then the maximum value of the function at sin x = 1, will be
Maximum value = 5/4 + 1
Maximum value = 9/4
Then the minimum value of the function at sin x = –1, will be
Minimum value = –5/4 + 1
Minimum value = –1/4
In the interval of (0, π/2), the function is decreasing.
And the range of the function will be [–1/4, 9/4].
More about the sine function link is given below.
https://brainly.com/question/3876065
#SPJ2
hii please help i’ll give brainliest
Answers
Answer:
-19
Step-by-step explanation:
Answer:
-19
hope it helps. Plz mark brainliest!
explanation:
To find its opposite, change the negative sign to a positive sign. The answer is that the opposite of 19 is -19.
Which side lengths form a right triangle?
Choose all answers that apply:
Answers
Answer:
A
Step-by-step explanation:
9, 12, 15 is a multiple of 3, 4, 5 which is a right triangle
Answer:
A. 9, 12, 15
Step-by-step explanation:
A. [tex]9^{2} +12^{2} =15^{2}[/tex]
B. [tex]6^{2} +2^{2}\neq\sqrt{38}^{2}[/tex]
C.[tex]3^{2} +9^{2} \neq \sqrt{91} ^{2}[/tex]
Math help me please/////
Answers
Answer:
C.
Step-by-step explanation:
A and D are incorrect because there is one outlier in the lower graph, and there are no signs of clusters on the graph, making B wrong as well. This leaves the only answer, C, which makes sense because there is a positive correlation of a line.
Find the product of 22.4 and 0.51
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Answer:
11.424 is the product of 22.4 x 0.51
what is the measure of angle 1?
Answers
Answer:
option a. 90°
angle 1=90°
hii please help i’ll give brainliest
Answers
The last answer choice
PLEASE HELP ASAP PLEASE HELP
Answers
HELP WILL MAKE BRAINLIEST
Answers
Answer:
x
Step-by-step explanation:
What is the volume of a sphere with a diameter of 7,5 cm, rounded to the nearest
tenth of a cubie centimeter
Answers
Answer:
179.59
Step-by-step explanation:
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Solve the system of equations 3x+2y=223x+2y=22 and -4x+3y=16−4x+3y=16 by combining the equations.
Answers
Answer:
(2, 8)
Step-by-step explanation:
Given the system of equation
3x+2y=22 ... *4
-4x+3y=16 .... *3
Using the elimination method
12x + 8y = 88
-12x + 9y = 48
Add
8y + 9y = 88+48
17y = 136
y = 136/17
y = 8
Recall that
3x+2y=22
3x+2(8)=22
3x + 16 = 22
3x = 22-16
3x = 6
x = 6/3
x = 2
Hence the required solution (x, y) is (2, 8)
A kind teacher gives you 20 cents for every question you get right, but you have to pay the
teacher 10 cents for every question you get wrong. After 30 questions you have made a
profit of $1.80.
a ) Form an equation with x representing the number of questions you got right.
b )Solve your equation to find how many questions you got right.
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Answer:
Let n be the number of questions you got right. Then
30-n equals the number of questions you got wrong.
So:
A) 20n-10(30-n)=180
30n-300=180
30n=480
n=16
30-n=14
B)You got 16 questions right and 14 questions wrong.
Please help
David has scored 86, 70, 79, 90, and 85 on his previous five tests. What score does he need on his next test so that his average (mean) is 84
Answers
Multiply 6 to both sides and then add everything together and then subtract i from the multiplied 86 which will get you 94.
Answer: 94
What is a possible solution to x ≥ −2?
Answers
Answer:
5
Step-by-step explanation:
If x+2y=12 and x-y=3 find the value of x+y
Answers
x-y=3
x=3+y
X+2y=12
(3+y) + 2y=12
3y+3=12
3y=9
Y=3
X-(3)=3
X=6
X+y
6+3=9
Suppose you add or subtract two quadratic trinomials that use the same variable. What are the possible classifications for the sum or difference? Explain.
Please help me asap. T.T
Answers
Answer:
quadratic monomial, quadratic trinomial, constant monomial, linear monomial, quadratic binomial, linear binomial.
Step-by-step explanation:
two quadratic trinomials each have a degree-2, degree-1, and degree-0 term. It is possible that the coefficients of all or some of the terms cancel each other while adding or subtracting the polynomials.
Answer:
Here is the answer. Hope this helps Sorry it's blurry but you have to click on it and you will see the answer
Step-by-step explanation:
If x = 7, what does y equal in the following equation? *
2x + 4y = -6
1) y = -2
2) y=-3
3) y=-4
4) y=-5
Answers
2x + 4y= -6
2(7) + 4y = -6
14 + 4y = -6
4y = -14 -6
y = -20/4
y = -5
find the slope of a line through the points (-1,5) and (7,-11)
Answers
Answer:
-2
Step-by-step explanation:
Find the surface area. Urgent!
Answers
Answer:
306 cm²
Step-by-step explanation:
Sorry if this is wrong doing mental math
Find the value of x in OQ. 5x-6
2x+9
Need help with this question asap!!
Answers
Answer:
[tex]\huge\boxed{\sf x = 5}[/tex]
Step-by-step explanation:
Since, the chord is being bisected by the diameter (being divided into two equal parts). Hence,
5x - 6 = 2x + 9
5x - 2x = 9 + 6
3x = 15
Divide both sides by 3
x = 15 / 3
x = 5
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807i just need help finding y thank you
Answers
Answer:
x=9.43mm
Step-by-step explanation:
H= A/C
H=9.15/cos(14)=9.43mm
Answer:
9.43
Step-by-step explanation:
If x = 2.28
pythagoras theory that a^2 + b^2 = c^2
so 9.15^2 + 2.28^2 = 88.920
[tex]\sqrt88.920[/tex]=9.429
$100 are shared between Adam and Hamza in the ratio 1:3.
A)
How many dollars did Adam receive?
How many dollars did Hamza receive?
Answers
Answer:
$25 for Adam and $75 for Hamza
Step-by-step explanation:
$100 will be divided to 3 + 1 = 4 parts
the dollars Adam received
= $100 × 1/4
= $25
the dollars Hamza received
= $100 × 3/4
= $75
-----------------------------------------------------------
the dollars Hamza give to Adam
= $75 × 25%
= $75 × 25/100
= $18.75
the dollars Adam have
= $25 + $18.75
= $43.75
the dollars Hamza have
= $75 - $18.75
= $56.25
the ratio
= 43.75：56.25
= 7：9
From the top of a light house 60 meters high with its base at sea level, the angle of depression to a boat is 15o. What is the distance of the boat from the foot of the light house?
Answers
Answer:
Distance between boat and light house = 223.88 meter (Approx.)
Step-by-step explanation:
Given:
Height of light house = 60 meters
Angle of depression to boat = 15°
Find:
Distance between boat and light house
Computation:
Using trigonometry application:
Tanθ = Perpendicular / Base
Tan 15 = Height of light house / Distance between boat and light house
0.268 = 60 / Distance between boat and light house
Distance between boat and light house = 60 / 0.268
Distance between boat and light house = 223.88 meter (Approx.)
State if the triangles in each pair are similar. Remember a) AA/SAS/SSS
b) prove it. C) write a similarity statement.
Answers
Note how we have a segment that is also 4 units long in the other triangle; however, we won't use that one just yet. Instead, we'll go for the 2 unit segment. As it turns out, every piece of the triangle on the right side is half that of the left side triangle.
Segment ED is 2 units long. So AB and ED pair up
------------------------------
BC is 8 units long; DF is 4 units long (half of BC). So BC and DF pair up
I started at A, went to B, then to C in that exact order marking the side lengths of 4 and 8 respectively. At the same time for the other triangle, I started at E, moved to D, then to F recording the side lengths 2 and 4
So A pairs up with E, B pairs with D, and C pairs with F
Therefore, triangle ABC is similar to triangle EDF. The order is very important so that the points line up and correspond in the proper manner.
I used the SSS (side side side) similarity theorem to prove the triangles similar. This theorem says that if the sides are in proportion to one another, then the triangles are similar.
A biologist was sitting near a pond and noticed a large number of dragonflies. He also saw both frogs and fish trying to eat the
dragonflies. He counted a total of 89 fish, frogs, and dragonflies. He noticed that there were four times as many dragonflies as fish and
that the frogs were five more than twice the number of fish
Answers
89 /3
frogs = 29.6
fish = 29.6
dragonflies = 29.6
all of them equal 89
a = fish = 12
b = frog = 29
c = dragonflies = 48
a + b + c = 89
c = 4a (four times as many dragonflies as fish)
b = 2a + 5 (frogs were five more than twice the number of fish)
Then substitute for b and c in the big equation:
a + (2a + 5) + 4a = 89
Combine like terms:
7a + 5 = 89
Subtract 5 from both sides:
7a = 84
Divide both sides by 7:
a = 12
Now use this to solve for b and c
c = 4(12) = 48
b = 2(12) + 5 = 24 + 5 = 29
Please let me know if you have any questions.
Help plz and the first and second options are.
First : any side,any two side,any three side
Second: less the. 90 degrees,greater then 90 and exactly 90
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Second: Exactly 90°
BAC ~ DEC
x = ___ units
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Given:
[tex]\Delta BAC\sim \Delta DEC[/tex]
To find:
The value of x.
Solution:
We have,
[tex]\Delta BAC\sim \Delta DEC[/tex]
The corresponding parts of similar triangles are proportional.
[tex]\dfrac{AB}{ED}=\dfrac{AC}{EC}[/tex]
On substituting the values, we get
[tex]\dfrac{24}{56}=\dfrac{2x}{3x+5}[/tex]
[tex]\dfrac{3}{7}=\dfrac{2x}{3x+5}[/tex]
[tex]3(3x+5)=2x(7)[/tex]
[tex]9x+15=14x[/tex]
Subtract [tex]9x[/tex] from both sides.
[tex]15=14x-9x[/tex]
[tex]15=5x[/tex]
[tex]\dfrac{15}{5}=x[/tex]
[tex]3=x[/tex]
Therefore, the value of x is 3 units.
I did not pay attention to the class- so can someone explain how to do dis type of problem- and the answers-
Answers
which questions ..??????
Farid checked the prices of 5 items available for purchase in the cafeteria. The prices were:
$6.00$8.00$6.00$2.00$4.00
What was the median price of the items?
MEAN AND MEDINA
Answers
Answer:
Mean is 5.2 Median is $6.00
Step-by-step explanation:
To find mean u have to find the "average" whereby u add all the numbers and divide by the number of numbers.
($2+$4+$6+$6+$8)= $26. Then since there are 5 numbers in all u divide by 5.
$26÷5 =5.2 5.2 is the median.
Median is the middle number. To find it u have to rearrange the numbers from smallest to largest and find the middle number.
$2, $4, {$6,} $6, $8
$6 is the median.
How many combinations with repetition are allowed if n = 5 and r = 3?
120
125
10
35
Answers
Answer:
35
Step-by-step explanation:
Since repetition is allowed, we use the equation
((n+r-1)!/(r!(n-1)!) = 7!/(3!x4!) = 35