Answer:
Solution to Problem 1:
Use the fact that the sum of all three angles of a triangle is equal to 180 o to write an equation in C.
A + B + C = 180 o
Solve for C.
C = 180 o - (A + B) = 43 o
Use sine law to write an equation in b.
a / sin(A) = b / sin(B)
Solve for b.
b = a sin (B) / sin(A) = (approximately) 5.4 cm
Use the sine law to write an equation in c.
a / sin(A) = c / sin(C)
Solve for c.
c = a sin (C) / sin(A) = (approximately) 7.1 cm
Problem 2
The angle of elevation to the top C of a building from two points A and B on level ground are 50 degrees and 60 degrees respectively. The distance between points A and B is 30 meters. Points A, B and C are in the same vertical plane. Find the height h of the building(round your answer to the nearest unit).
diagram problem 2
Solution to Problem 2:
We consider triangle ABC. Angle B internal to triangle ABC is equal to
B = 180 o - 60 o = 120 o
In the same triangle, angle C is given by.
C = 180 o - (50 o + 120 o) = 10 o
Use sine law to find d.
d / sin(50) = 30 / sin(10)
Solve for d.
d = 30 *sin(50) / sin(10)
We now consider the right triangle.
sin (60) = h / d
Solve for h.
h = d * sin(60)
Substitute d by the expression found above.
h = 30 *sin(50) * sin(60) / sin(10)
Use calculator to approximate h.
h = (approximately) 115 meters.
Problem 3
A triangle ABC has side a = 12 cm, side b = 19 cm and angle A = 80 o (angle A is opposite side a). Find side c and angles B and C if possible.(round answers to 1 decimal place).
Solution to Problem 3:
Use sine law to write an equation in sin(B).
a / sin(A) = b / sin(B)
Solve for sin(B).
sin (B) = (b / a) sin(A) = (19/12) sin(80) = (approximately) 1.6
No real angle B satisfies the equation
sin (B) = 1.6
The given problem has no solution.
Problem 4
A triangle ABC has side a = 14 cm, side b = 19 cm and angle A = 32 o (angle A is opposite side a). Find side c and angles B and C if possible.(round answers to 1 decimal place).
Solution to Problem 4
Use sine law to write an equation in sin(B).
a / sin(A) = b / sin(B)
Solve for sin(B).
sin (B) = (b / a) sin(A) = (19/14) sin(32) = (approximately) 0.7192
Two angles satisfy the equation sin (B) = 0.7192 and the given problem has two solutions
B1 = 46.0 o and B2 = 134 o
Solution 1: Find angle C1 corresponding to B1
C1 = 180 - B1 - A = 102 o
Solution 1: Find side c1 corresponding to C1
c1 / sin(C1) = a / sin(A)
c1 = 14 sin(102) / sin(32) = (approximately) 25.8 cm
Solution 2: Find angle C2 corresponding to B2
C2 = 180 - B2 - A = 14 o
Solution 2: Find side c2 corresponding to C2
c2 / sin(C2) = a / sin(A)
c1 = 14 sin(14) / sin(32) = (approximately) 6.4 cm
Exercises
1. A triangle ABC has angle A = 104 o, angle C = 33 o and side c = 9 m. Solve the triangle ABC by finding angle B and sides a and b.(round answers to 1 decimal place).
2. Redo problem 2 with the distance between points A and B equal to 50 meters.
Solutions to Above Exercises
1. B = 43 o, a = 16.0 m , b = 11.3 m
2. 191 meters.
More References and Links to Sine and Cosine Laws
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Sine Law Calculator and Solver.
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a little help would be nice
Answer:
13). -2x³ + x² + 1 14). x + 10y - 10z 15). -2x³ + x² + 1
Step-by-step explanation:
13). (x³ - x² + 4) - (3x³ - 2x² + 3)
= x³ - x² + 4 - 3x³ + 2x² - 3
= x³ - 3x³ - x² + 2x² - 3 + 4
= -2x³ + x² + 1
14). (3x + 4y - 3z) - (2x - 6y + 7z)
= 3x + 4y - 3z - 2x + 6y - 7z
= 3x - 2x + 4y + 6y - 3x - 7z
= x + 10y - 10z
15). (x³ - x² + 4) - (3x³ - 2x² + 3)
= x³ - x² + 4 - 3x³ + 2x² - 3
= x³ - 3x³ - x² + 2x² + 4 - 3
= -2x³ + x² + 1
In her metalwork class, Anja cut a square of
tin, of edge 3.7 cm, from a larger square of
edge 6.3 cm. What area of tin was left?
Given:
Anju cut square of tin, of edge 3.7 cm, from a larger square of edge 6.3 cm.
To find:
The area of the remaining tin.
Solution:
Area of a square is:
[tex]Area=a^2[/tex]
Where, a is the edge of the square.
Area of the smaller square is:
[tex]A_1=(3.7)^2[/tex]
[tex]A_1=13.69[/tex]
Area of the larger square is:
[tex]A_2=(6.3)^2[/tex]
[tex]A_2=39.69[/tex]
The area of the remaining tin is:
[tex]A=A_2-A_1[/tex]
[tex]A=39.69-13.69[/tex]
[tex]A=26[/tex]
Therefore, the area of the remaining tin is 26 sq. cm.
Please help me with this please ASAP
Answer:
h: 4
LA: 80
SA: 112
Step-by-step explanation:
Solve for h, and then use the previous equations.
A function is defined by the rule f(x) = 11 - 2x. What is the value of f(-3) ?
Answer:
17
Step-by-step explanation:
11 - 2(-3) = 11 + 6 = 17
should put -3 where x is
Sangsters sells staples in packs of 500 Staples for $1,250 and 1000 Staples for $3,000. Which pack is the better value for money? Justify your answer.
Answer:
Step-by-step explanation:
I want to know what kind of stables are these? Are they made out of gold?
$1250 / 500 stables verses $3000 / 1000 stables
$2.5 per stable $3 per stable
Both packs are too expensive but $2.5 per stable isthe better value.
A store is going out of business. Everything is
marked down 40%. How much do you pay for an item
that used to cost $150?
A. $90
B. $110.50
C. $40
jose paid $47.00 for 4 movie tikits. each tiket cost the same amount . what was the cost of each movie tiket in doller and cents?
What is the probability of rolling a 1 ora 4 on a number cube labeled 1 through 6?
Answer:
For each number, there is a 1/6 probability of rolling it (so 1/6 for the 1 and also 1/6 for the 4).
This means that the probability of rolling either a 1 or a 4 on a given roll is
1 /6 + 1 /6 = 2/6 = 1/3
hope this answer helps you.....
Answer:
Is 1/6
Step-by-step explanation:
Help I need this tomorrow
9. Make Sense and Persevere The graph shows
the number of gallons of water in a large tank
as it is being filled. Based on the trend line,
predict how long it will take to fill the tank
with 375 gallons of water.
Answer:
About 18 minutes
Step-by-step explanation:
a dice is rolled 60 times, what is the probability of it landing on 4
Find the normal approximation to the chance that the face with six spots appears between 9, 10, or 11 times.
The exact chance that the face with six spots appears 9, 10, or 11 times?
my solution; in one roll of the die P(6 spots)=16 In 60 rolls of the die the expected number of times the face with 6 spots appears is given by E(X)=Mean=606=10 times.
SE(6spots)=SD=SQR(606⋅56)=2.8868
Applying the normal approximation to the chance that the face with six spots appears 10 times, I obtain the following: mean = 10
Standard deviation=2.8868
Using the continuity correction of 0.5 the following z-scores are found: z1=(9.5−10)/2.8868=−0.1732 and z2=(10.5−10)/2.8868=0.1732 Subtracting the cumulative probabilities for the two z-scores gives 0.5688−0.4312=0.1376 which is the approximate chance that the face with six spots appears 10 times. find the six spots appears between 9,10, or 11?
The exact chance that the face with six spots appears 10 times is found from
60C10(16)10×(56)50=0.137 find six spots appears 9, 10 or 11 times
I SHALL REWARD THEE WITH BRAINLIEST Change -2Y - 2X = -6 to the slope intercept form of the equation of a line (I NEED EXPLANATIONS FOR FURTHER QUESTIONS I GET STUCK ON) :3 ty and hawwo
Answer:
y = -x + 3
Step-by-step explanation:
First of all, you need to memorize several forms of the equation of a straight line. Here you have -2y - 2x = -6 in "standard form" and want the equivalent equation in "slope intercept form," y = mx + b.
To get this, solve the first equation for y by dividing all three terms by -2:
y + x = 3.
Then solve this result for y:
y = -x + 3
This is the desired equation in slope-intercept form.
.........help.......me.......please
Answer:
145°
Step-by-step explanation:
180-35=145
Answer:
145°
Step-by-step explanation:
subtract 35 from 180
because a straight line is 180
180- 35
145°
to check,
add 35 and 145 to make sure it adds up to 180
it does.
How would I set this to 0?
Answer:
− 2 sin ( 0 ) ⋅ sin ( 0 ⋅ π /0 m ) + cos ( 0 ) ⋅ cos ( 0 ⋅ π /0 m ) = 0 is not an identity
Step-by-step explanation:
which number is equivalent to 2^3/3^3
Answer:
8/27
Step-by-step explanation:
Help me with this?!!!!
Answer:
14
Step-by-step explanation:
we can use sin(30⁰) to solve this and the units will be 14
What two numbers have a product of -54 and a sum of -3?
Answer:
-9 and 6
Step-by-step explanation:
Answer:
-9 and 6
Step-by-step explanation:
-9X6 is -54
and -9+6 is -3
Answer the question above
Answer:
BA
Step-by-step explanation:
The hypotenuse is the longest side or opposite the right angle.
Answer:
AB
Step-by-step explanation:
The pythagorean theorem is AC² + CB² = AB²
AB represents the hypotenuse
which of the following can be brisk? a.A gift from a relative b.A walk around town c.a bowl of soup d.A fall breeze
(Pick all of the following hint: there is more than one.)
Answer:
A fall breeze and a bowl of soup I might say.
What are the solutions to this equation?
16x2 + 9 = 25
Answer:
Step-by-step explanation:
Solution
= −1
= 1
Answer: x=-1,1
Step-by-step explanation:
16x^2+9=25 first we subtract 9 from the right and left sides.
16x^2=16
Divide both sides by 16 to isolate x
x^2=1
Take the square roots of both sides to isolate x completely.
x=1,-1
helps plz,
The figure shows a kite inside a rectangle. Which expression represents the area of the shaded region?
A. 2x^2
B. 4x^2
C. 6x^2
D. 8x^2
Thanks!!
[tex] \huge \mathrm{Answer࿐ }[/tex]
Fig - 1 : Rectangle
length = 3x + x = 4x width = x + x = 2x[tex] \boxed{\mathrm{Area = length \times width}}[/tex]
[tex]4x \times 2x[/tex][tex]8 {x}^{2} [/tex]_____________________________
Fig - 2 : Kite
[tex] \boxed{\mathrm {Area = \dfrac{1}{2} \times d_1 \times d_2 }}[/tex]
[tex] \dfrac{1}{2} \times 4x \times 2x[/tex][tex]4 {x}^{2} [/tex]_____________________________
Area of shaded region :
Area of rectangle - Area of kite [tex]8 {x}^{2} - 4 {x}^{2} [/tex][tex]4 {x}^{2} [/tex]So, Correct option is B. 4x²
_____________________________
[tex]\mathrm{ \#TeeNForeveR}[/tex]
Nadia needs 2/5 cup of orange juice for a punch recipe. She will double the recipe to make punch for a party. Which statement is true?
Answer:
Step-by-step explanation:
There's not a lot to go on with the details provided in the question, but based on all you said, if there isn't more to the question, then the true statement is the fact that Nadia needs 2/5 cup of orange juice for punch recipe.
Twice that amount is 4/5, and logically, that can't suffice in a party, except it's a party of 3, maybe 5 people. I'm assuming the people in the party would be much more than that. Makes the fraction impossible
find the mole fraction of benzene and toluene in solution containing
(a) equal mass of each
(b) equal molecules of each
Answer:
Hello There!!
Step-by-step explanation:
I think the answer is possibly (b) equal molecules of each .
hope this helps,have a great day!!
~Pinky~
Find (x-4) (2x +1) using table of products. Write in standard form
Answer:
[tex]2x^{2} - 7x - 4[/tex]
Step-by-step explanation:
Give Me Brainllest
Answer:
Your welcome ;)
Step-by-step explanation:
hi someone fill out this chart pls. will give brainly if u do it correctly
Answer:
1 → 10
2 → 1000
3 → 16
4 → 64
5 → 6
6 → 36
7 → 7
8 → 343
Given the following function, find the x and y intercepts (from left to right), vertex, and axis of symmetry.
Function: f(x)=(x+2)(x−4)
Answer:
ik the answer its at the tip of my tounge im so sorry wish i could help
Step-by-step explanation:
The phases of the moon are periodic and repetitive. A new moon occurs when no moon is visible to an observer on
Earth. During the first quarter, half of the side of the moon facing the Earth is visible. During a full moon the entire
side of the moon is visible. During the last quarter the other half of the side of the moon facing Earth is visible.
The U.S. Naval Observatory lists the following dates for phases of the Moon in the year 2008.
Date Moon Phase x: Days since y: The Amount of
Jan. 8
Moon Visible
Jan 8 New
JO
10
Jan 15 1st quarter
7
0.5
Jan 22 Full
13
1
Jan 30 Last quarter 22
10.5
Feb 7 New
30
0
Feb 14 1st quarter 37
10.5
Feb 21 Full
44
1
Feb 29 Last quarter 52
10.5
Mar 7 New
59
o
Mar 14 (1st quarter
66
0.5
Answer:
It's A
Step-by-step explanation:
Got it right on the practice :)
Based on the data presented , the answer is that Yes, it show repeated and periodic behavior. and thus the data indicate that a sine regression is appropriate in this case.
What leads to a new moon phase?This occurs as our Moon is said to orbits around Earth. the side of the moon that is facing the Sun is said to be illuminated due to the sun's brightness, just like when the Earth's daylight side is also said to be illuminated by the Sun.
We tend to have a “new Moon” only when our Moon is said to orbit around the Earth and thus moves it between Earth and the Sun.
See options below
Using the information above, plot the data points. Does this data indicate that a sine regression may be appropriate in this case?
a. Yes, it shows repeated and periodic behavior.
b. Yes, it shows a curve increasing from left to right.
c. No, the points are random.
d. No, the points depict a parabola.
Learn more about phases of the moon from
https://brainly.com/question/13538936
I really need help please
Answer:
Step-by-step explanation:
This is the answer
Given that the area of the whole rectangle is 48 square units, find the area of (I).
So say someone did 1000 push ups a day for 8 years 2920 days in 8 years and you want to do the same amount but in 2 months how many would you have to do a day
Answer:
48,667 if you round it..
Step-by-step explanation:
1000x2920 = 2,920,000
divided by 2 months
2,920,000/2 = 1,460,000
and theres 30-31 days in a month
1,460,000/30 = 48,666.67
what is the least common denominator of 3/1+8/4
Answer:
4355646
Step-by-step explanation:
45345
Answer:
least common denominator is 4
Step-by-step explanation:
3/1+8/4=20/4 which is 5
