1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Romashka [77]
3 years ago
15

QF Q8.) Solve the triangle.

Mathematics
2 answers:
Anuta_ua [19.1K]3 years ago
5 0
A triangle solver tells you
  C = 85°
  b ≈ 8.4
  c ≈ 10.4

From the sum of angles of a triangle, 
  C = 180° -42° -53° = 85°

From the law of sines
  b = sin(53°)/sin(42°)*7 ≈ 8.355
  c = sin(85°)/sin(42°)*7 ≈ 10.422
  

svetlana [45]3 years ago
4 0
Comment
To start this question after finding C, you need to use the Sin Law for solving lengths (or angles)  in triangles that are not right angle triangles

That's not exactly good news. The Sin law can return no solutions, or one solution or 2 solutions. 

The programmer only gave you the opportunity of offering 1 solution.That likely means that there is only one solution or none.

Step One
Solve for C
Givens
A  = 42°
B = 53°
All triangles have 180° as the sum of their angles.

A + B + C = 180°         Substitute for A and B
42° + 53° + C = 180°   Combine the like terms on the left
95° + C = 180°            Subtract 95 from 180
C = 180° - 95°
C = 85°

Step Two
Find b
Note: You must use the Sin Law here.
Sin(A) / a = Sin(B)/b            Cross multiply.
b * Sin(A) = a* Sin(B)           Divide by Sin(A)
b = a * Sin(B) / Sin(A)

Substitute the known parts into the expression above.

b = 7 * sin(53) / Sin(42)
b = 7 * 0.7986 / 0.6691
b = 8.3548

Step Three
Find c
Comment: as soon as possible it is a good idea to switch to the cos law. It gives only one solution per a given set of numbers.

a = 7
b = 8.3548
C = 85

c^2 = a^2 + b^2 - 2*a*b * Cos(C)
c^2 = 7^2 + 8.3548^2 - 2*7*8.3548 * cos(85)  
c^2 = 49  + 69.8027 - 2*7*8.3548*0.087156
c^2 = 118.8027 - 10.1944
c^2 = 108.6083                  Take the square root of both sides.
c = sqrt(108.6083)
c = 10.4215

Answers
C = 85°
b = 8.3548
c = 10.4215 

I leave the rounding to you.

Comment
Note: we did not eliminate the possibility of no solutions. That occurs if you find the height of the triangle using (in this case) angle B. 

Sin(53) = opposite (height) / hypotenuse (which would be a in this case).
hypotenuse = 7
Sin(53) = height / hypotenuse
0.7986 = height / 7
7 * 0.7986 = height
height = 5.5902

As long as h < a (in this case it is) there is 1 solution and the 0 solutions is eliminated. Technically, a purist would insist on making this test. If a<h then a would hang like a swinging lamp from C and would never touch AB. 

We have established that there is 1 solution, but maybe there are two. No that's not possible from the givens. 2 solutions would require that 2 sides and an angle be given. The given angle cannot be between the 2 sides. There might still be only 1 solution because a > b. If it is, then a can't swing across to meet AB in 2 places.

That's why, if all possible the cos law should be used.
You might be interested in
Joesl's father is 45. He is 15 years older than twice joe's age. How old Is joe?
tresset_1 [31]
Joe is 15, 45-15=30 30/2=15
6 0
3 years ago
The parallelogram below is being covered with carpet. The carpet is priced at $2.80 per square meter. How much will it cost to c
Sloan [31]

Answer:

<em><u>$79.38</u></em>

Step-by-step explanation:

Find the diagram of the question attached

Area of the parallelogram = Base * Height

Given

Base = 8.1m

Height = 3.5m

Area of the parallelogram = 8.1 * 3.5

Area of the parallelogram = 28.35m²

If the carpet is priced at $2.80 per square meter, then;

1m² = $2.80

28.35m² = x

x = 28.35 * 2.80

x = $79.38

<em><u>Hence the cost of the carpet is $79.38</u></em>

7 0
2 years ago
The length of a rectangle is 3 meters greater than 2 times the width. The perimeter of the rectangle is 30 meters.What is the le
faust18 [17]

Answer:

11 meters

Step-by-step explanation:

Lets say that  w = width of the rectangle, to start. If the length of the rectangle is 3 meters greater than 2 times the width, the length of the rectangle is equal to 3 + 2w.  

The perimeter of the rectangle is 2 * length of rectangle + 2 * width of the rectangle. With the perimeter being equal to 30 and width being w and length being 2w+3:

The perimeter of the rectangle is 2(w) + 2(2w+3) = 30.  

We first need to find out w first, which will give us the width of the rectangle. Taking it step by step, we get:

2w + 4w + 6 = 30

6w + 6= 30

6w = 24 which is done by subtracting both sides by 6 to put the variables on one side and the values on the other side

w = 4 which is done by dividing 6 on both sides

Ultimately, this gets width to be 4 meters. Now that we found the width, we need to plug w = 4 into the equation we set up for length which is 2w+3.

That being said, the ANSWER is:

length of rectangle = 2(4)+3 = 11 meters

Hope this helps! :)

4 0
3 years ago
Hunter read a total of 22 books over 11 months. If Hunter has read 42 books so far, how
Mamont248 [21]
21 months. Hope this helps!
5 0
2 years ago
If jamie has $5 and purchases a soda for $1.15 how much change does jamie get back
ArbitrLikvidat [17]
Jamie get back:5-1.15
=$3.85
5 0
3 years ago
Other questions:
  • A snack food manufacturer buys corn for tortilla chips from two cooperatives, one in Iowa and one in Illinois. The price per uni
    10·1 answer
  • Ice skates on sale for 25% off cost $45. What is the regular price of the skates? a. $56.25 c. $70 b. $60 d. $80
    12·2 answers
  • Professor Halen teaches a College Mathematics class. The scores on the midterm exam are normally distributed with a mean of 72.3
    9·1 answer
  • Emily wants to know the volume of a beach ball. She deduces that the beach ball has diameter of 12 inches, and then uses the fol
    13·1 answer
  • Plz help! <br><br> What is the volume of the composite figure?!
    15·1 answer
  • Solve the following inequality: 30 ≥ -30 – 6x *
    14·1 answer
  • 2. The line that passes through the points (-6, p)
    6·1 answer
  • What is the area of the parallelogram shown below?<br><br> ___ <img src="https://tex.z-dn.net/?f=units%5E%7B2%7D" id="TexFormula
    15·1 answer
  • 2p-q=0 find the subject formula for p and q
    14·1 answer
  • What is 6.1 x 10 to the power of 4 in standard form
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!