Find the missing side and angle measures in triangle ABC. Round your answers to the nearest tenth.
The measure of angle B is approximately
__.
The measure of angle C is approximately
__.
The length of side AB is approximately
___units.
Answers
Answer:
[tex]m\angle B\approx 80.27^\circ\text{ and } m\angle C\approx 59.73^\circ[/tex]
Side AB measures approximately 20.15 units.
Step-by-step explanation:
We can use the Law of Sines, given by:
[tex]\displaystyle \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}[/tex]
Since we already know ∠A and a, we can use it to determine our other measures.
We know that b is 23. Substitute:
[tex]\displaystyle \frac{\sin 40^\circ}{15}=\frac{\sin B}{23}[/tex]
Solve for ∠B:
[tex]\displaystyle \sin B=\frac{23\sin 40^\circ}{15}[/tex]
We can take the inverse sine of both sides:
[tex]\displaystyle m\angle B=\sin^{-1}\frac{23\sin 40^\circ}{15}[/tex]
Use a calculator (make sure you're in Degrees mode!):
[tex]m\angle B\approx 80.27^\circ[/tex]
The interior angles of a triangle must total 180°. Hence:
[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex]
Substitute in known values:
[tex](40^\circ)+(80.27^\circ)+m\angle C=180^\circ[/tex]
Therefore:
[tex]m\angle C\approx 59.73^\circ[/tex]
Lastly, to find AB or c, we can use the Law of Cosines:
[tex]c^2=a^2+b^2-2ab\cos(C)[/tex]
a = 15, b = 23, and to prevent rounding errors, we will use the exact value for C. Recall that we know that:
[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex]
Using the exact value for ∠B, we acquire:
[tex]40^\circ+\displaystyle \sin^{-1}\frac{23\sin40^\circ}{15}+m\angle C=180^\circ[/tex]
Therefore:
[tex]\displaystyle m\angle C=\left(140-\sin^{-1}\frac{23\sin40}{15}\right)^\circ[/tex]
Substitute:
[tex]\displaystyle c^2=(15)^2+(23)^2-2(15)(23)\cos\left(140-\sin^{-1}\frac{23\sin40^\circ}{15}\right)[/tex]
Simplify and take the square root of both sides.
[tex]\displaystyle c=\sqrt{754-690\cos\left(140-\sin^{-1}\frac{23\sin40^\circ}{15}\right)}[/tex]
And use a calculator:
[tex]c\approx 20.15[/tex]
Answer:
Hi! The person above is actually correct, just that it needed to be rounded to the nearest tenth. Check the picture for confirmation. Hope this helped <3
Step-by-step explanation:
The measure of angle B is approximately
80.3
The measure of angle C is approximately
59.7
The length of side AB is approximately
20.2
I got it correct on Edmentum/Plato
Related Questions
can anyone simplify 5(x-6)
Answers
Answer:
5x - 30
Step-by-step explanation:
5(x-6)
Distribute the 5 to both terms inside the parentheses
5*x - 5*6
5x - 30
Answer:
5x-30
Step-by-step explanation:
use the distributive property
7.865 rounded to the nearest whole number
Answers
Answer:
8
Step-by-step explanation:
Since the first decimal place is greater than 5, it rounds to 8, because 8 is the next whole number to 7.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Which equation represents a line which is perpendicular to the line 6x+y=-4
Answers
Answer:
y = 1/6x - 4
Step-by-step explanation:
y = -6x - 4
current slope is -6 so the slope of a line perpendicular would be 1/6
y = 1/6x - 4
Rationalize 1/√18
Will Mark as Brainliest for the best
Answers
Answer:
[tex]\frac{\sqrt{2} }{6}[/tex]
Step-by-step explanation
[tex]\frac{1}{\sqrt{18} } \\\frac{1}{\sqrt{18} } *\frac{\sqrt{18} }{\sqrt{18} } \\\frac{1*\sqrt{18} }{(\sqrt{18} )^2} \\\frac{1\sqrt{18} }{18} \\\frac{3\sqrt{2} }{18} \\\frac{\sqrt{2} }{6}[/tex]
21 POINTS!! Thank you so much!! There’s also things on my page worth lots points points as well! So if you could help with those that would be awesome!!
Answers
Answer:
Second one
third one
fifth one
last one
Step-by-step explanation:
Based on the x intercepts we can write
a(x+1)(x-5)
where a is some constant
solve for a by plugging in some coordinates
let's plug in (1,-8)
-8=a(1+1)(1-5)
-8= -8a
a=1
therefore the quadratic is (x+1)(x-5)
expand this
x²-4x-5
To find out where something is decreasing/increasing it's easiest to take the first derivative
x²-4x-5= 2x-4
set this equal to 0
2x-4=0
2x=4
x=2
Which means that our two intervals are
(-∞,2)U(2,∞)
plug in any values in the intervals to see whether or not the function is increasing/decreation
Let's plug in 0 for (-∞,2)
2(0)-4
-4
It's negative so it's decreasing on this interval
DO the same thing with the other one
let's plug in x=3
2(3)-4
2
this is positive so it's increasing on this interval
Go back to the critical value of x=2 and plug this into the equation to find the max/min
(2+1)(x-5)= -9
This is a minimum because the cofeccient for the degree is positive
For the limit one notice that we have a positive, even degree which means the end behavior is positive, positive
what this means is as x approaches negative infinity it's infinity
and as x approaches infinity it's infinity
What is the reflection of point P (2, -7) over the x-axis
Answers
Answer:
(2,7) I think
Step-by-step explanation:
Answer:
(2,7)
Step-by-step explanation:
It's funny, this is the exact topic I just learned.
Ok, 2,-7 would be in the fourth quadrant (IV).
So using this information if we want to reflect it over the x axis, the point would just got over the x axis in quadrant 1. We know that quadrant 1 is (++) so the ordered pair MUST be positive. Hence the answer of (2,7)
Hope this helps!
whats the anserw plz (8x+10y)+(-4x-3y) i need help!!!
Answers
Answer:
me :- mighty assassin-,-
xd
Which is the degree measure of an angle whose tangent is 1.19? Round the answer to the nearest whole number. A. 48° B. –48° C. 50° D. –50°
Answers
9514 1404 393
Answer:
C. 50°
Step-by-step explanation:
The angle whose tangent is 1.19 is ...
arctan(1.19) ≈ 49.9585° ≈ 50°
The 50° measure of an angle whose tangent is 1.19.
What is tangent?Tangent in geometry, is defined as "a line or plane that touches a curve or curved surface exactly at one point" .
According to the question,
The degree measure of an angle whose tangent in 1.19.
In order to an angle only if arctan(119) = 49.9585 ≈ 50.
Hence, the 50° measure of an angle whose tangent is 1.19.
Learn more about Tangent here
https://brainly.com/question/20725027
#SPJ2
Solve for xxx in the diagram below.
Answers
5 times 6 = 30
54 plus 6 =60
and that is a 90 degree angel
could u help me last part :)
Answers
Answer: 288pi in cubed
Step-by-step explanation: because area of a circle is pir^2 so 36*8=288
Explanation:
Volume Formula= piR^2h (R= Radius and H= Height)
So pi*6^2*8 gets you 288pi ^3
Keep the formula in mind to help you with further problems.
Hope this helps you. If available please give me a branliest. It would be much appreciated!
- Mathhotdog •~•
The circumference of a circle is 125.6
kilometers. What is the circle's radius?
Answers
Answer:
r = 20 km
General Formulas and Concepts:
Symbols
π (pi) ≈ 3.14Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityGeometry
Circumference of a Circle Formula: C = 2πr
r is radiusStep-by-step explanation:
Step 1: Define
Identify variables
C = 125.6 km
Step 2: Solve for r
Substitute in variables [Circumference of a Circle Formula]: 125.6 km = 2(3.14)rMultiply: 125.6 km = 6.28r[Division Property of Equality] Divide 6.28 on both sides: 20 km = rRewrite: r = 20 kmAnswer:
197.29
Step-by-step explanation:
Multiple the circumfernece by 3.14 and then divide that number by 2.
please help me i have 5 minutes left: )! ill give Brainliest thanks<3
Answers
Answer:
B
Step-by-step explanation:
B
Which of the following is equivalent to the expression below?
log 4-log 24
Answers
Answer:
log (1/6)
Step-by-step explanation:
Using the property that log a - log b = log(a/b), we get that log 4 - log 24 = log(4/24) = log (1/6)
I hope this helps! :)
Question 12
A tree is standing next to a 40 foot high building. The tree has an 18 foot shadow, while the building has a 16 foot shadow. How tall is the tree rounded to the nearest foot?
А
42 feet
B
36 feet
c
45 feet
D
7 feet
2021 Illuminate Education Inc
Answers
Answer:
A
Step-by-step explanation:
y = 3x - 1
3x - y = 9
X=
A) x = 123, y = 4 4
B) x=3, y = 0
C) No solution
D) Infinitely many solutions
Answers
Answer:
no solution.
Step-by-step explanation:
given that, y = 3x-1
so,
in equation, 3x-y = 9
putting the value of y here,
3x-(3x-1) = 9
3x-3x+1 = 9
3x and 3x is cancelled.
hence, no solution
The graph of f(x) = |x – h| + k contains the points (–6, –2) and (0, –2). The graph has a vertex at (h, –5). Describe how to find the value of h. Then, explain how this value translates the graph of the parent function.
Answers
Answer:
ty
Step-by-step explanation:
mtj
2. Find the base of a triangle which has an area of 2 1/4 square inches, and a height of 1/8 in.
Answers
Answer:
36 inches
Step-by-step explanation:
Given data
Area of triangle =2 1/4 square inches
Area =9/4 square inches
Height of triangle =1/8 inches
We know that the expression for the area of triangle is
Area = 1/2Base *Height
9/4=1/2*Base *1/8
9/4=Base/16
Cross multiply
16*9=Base*4
144=Base*4
Base =144/4
Base=36 inches
Please answer
Evaluate 60st when s = 5 and t = -3.7
Answers
Answer:
[tex]60st \\ = (60 \times 5 \times - 3.7) \\ = - 1110[/tex]
Answer:
-1110
Step-by-step explanation:
given:
s = 5
t = -3.7
to find
60st
=60*s*t
=60*5*(-3.7)
=300*-3.7
=-1110
Need help ASAP, willing to give brainliest to the best answer!
Answers
Answer:
Question number 1: 70
Question number2: 0
Question number 3: Mike team
Step-by-step explanation:
Question number 1: Just add all of the numbers together and you will get 70 as your answer.
Question number 2: Becuase everyone in the team has scored at least 1 point or greater.
Question number 3: Mike's team becuase he and his team has the most points out of all the other teams.
Hope this helps :D
If p and q vary inversely and p is 9 when q is 16, determine q when pis equal to 18.
Answers
Answer:
[tex]p \: \alpha \: \frac{1}{q} \\ p = \frac{k}{q} \\ k \: is \: a \: constant \: of \: proportionality \\ when \: p \: is \: 9.. \: \: q = 16 \\ 9 = \frac{k}{16} \\ k = 144 \\ when \: p \: is \: 18 : \\ 18 = \frac{144}{q} \\ q = \frac{144}{18} \\ q = 8[/tex]
How does the range of g(x)=6/x compare with the range of the parent function f(x)=1/x?
Answers
Answer:
The range of both [tex]f(x)[/tex] and [tex]g(x)[/tex] is all nonzero real numbers.
Step-by-step explanation:
The range of the function is the set of real number for [tex]y[/tex]. The rational function of the form [tex]y = \frac{a}{x}[/tex], where [tex]a[/tex] is a constant, has a range represented by the subset of nonzero real numbers. This is: [tex]Ran\{f(x)\} = \mathbb{R}-\{0\}[/tex]
Hence, the correct answer is: The range of both [tex]f(x)[/tex] and [tex]g(x)[/tex] is all nonzero real numbers.
Solve for x in the equation
Answers
Answer:
its the first one
Step-by-step explanation:
a bookcase is 500mm wide how many of these bookcase will fill a
space 2m wide
Answers
I think 4 but I could be wrong
WILL GIVE BRANLIEST!!! pls help tysm!!!
Answers
HELPP PLEASEEE thanks!
Answers
Answer:
about 1587
that is the answer to the question
Step-by-step explanation:
I just typed it in a calculator
Answer: D
Step-by-step explanation:
Area is pi x r^2
Diameter is 2r
46.7/2 = 23.35
3 x 23.35^2 = 1635.67 or closest to D
Is -33.1 a whole number
Answers
Answer:
No
Step-by-step explanation:
This is because it's part of a whole. It has to be an integer to be whole.
Answer:
no because Whole numbers include positive integers along with 0 and also Whole numbers include natural numbers that begin from 1 onwards and also this a negative are not considered as a whole number so its a no
Step-by-step explanation:
(NEED HELP ASAP) The map is similar to the map from the previous unit. The x-axis runs from -110 to +110. For the y-axis, the values run from -80 to +80. Each tick mark on the axes has the value of 5 m (so each square on the grid represents 10 m). The additional path, Archimedes Alley has been added to the map.
The standard form for one of the three equations is 9x - 20y - 900 = 0.
i) Determine the x- and y-intercepts for the line.
ii) Identify its equivalent equation in slope y-intercept form.
iii) Explain how you chose the equation in slope y-intercept form.
Answers
I got it partially right I think but I need help !
Answers
Answer:
U got it correct
Step-by-step explanation:
what is the value of x? 0 = x/6 - 3
Answers
Answer:
18 = x
Step-by-step explanation:
0 = x/6 - 3
Add 3 to each side
0+3 = x/6-3+3
3 = x/6
Multiply by 6 on each side
3*6 = x/6*6
18 = x
Jeanne goes to the city park every 7 days for walk. Susan goes to the park every 10 days. If they both went to the park today and met each other, after how many days again will they be in the park and meet again?
Answers
Answer:
70 days
Step-by-step explanation:
We solve using Lowest Common Denominator method
Find and list multiples of each number of days for a walk until the first common multiple is found. This is the lowest common multiple.
Jeanne goes to the city park every 7 days for walk. Susan goes to the park every 10 days.
Hence:
Multiples of 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84
Multiples of 10:
10, 20, 30, 40, 50, 60, 70, 80, 90
Therefore,
LCM(7, 10) = 70
Therefore, the number of days in which they will they be in the park and meet again is 70 days
