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
R is the midpoint of OP and QR is perpendicular to OP in the diagram below
dezoksy [38]

Answer:

24 in

Step-by-step explanation

Using pythagorean theorem, since OP is 20 inches and has a midpoint. RP= 10 and OR=10. The hypotenuse is given as 26 so do 26^2=10^2+a. 676= 100+a^2, subtract 100 from both sides. square root of 576 is 24

7 0
3 years ago
What is the product of -1/2 x 1/8 in simplest form
hjlf

Answer: Edit: -0.0625

Step-by-step explanation:

3 0
3 years ago
Evaluate the geometric series
Schach [20]

Your multiplying by -4 each time

-1x-4=4

4x-4=-16

-16x-4=64

3 0
3 years ago
Show whether or not y=x+3 is tangential to the curve y^2=x​
wolverine [178]

The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.

y² = x

Take the derivative of both sides with respect to x, assuming y = y(x) :

2y dy/dx = 1

dy/dx = 1/(2y)

Solve for y when dy/dx = 1 :

1 = 1/(2y)

2y = 1

y = 1/2

When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.

This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :

x = y²   ⇒   y = y² + 3   ⇒   y² - y + 3 = 0

has no real solution for y.

3 0
2 years ago
Given: TSR and QRS are right angles; T ≅ Q
allsm [11]

Answer:

The answer is number (2) ⇒ because of the AAS congruence theorem

Step-by-step explanation:

* Lets use the information to solve the problem

- In the given triangles TSR and QRS

# We have a common side RS or SR

# Two right angles TSR and QRS

# m∠T = m∠Q ⇒ given

* So we have two pairs of angles and one common side, lets

 revise the cases of congruence

- SSS  ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and

 including angle in the 2nd Δ

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ

 ≅ 2 angles and the side whose joining them in the 2nd Δ

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles

 and one side in the 2ndΔ

* Now lets read the statements and write the missing

Step 1: m∠TSR = m∠QRS = 90° ⇒ because all right angles are congruent

Step 2: m∠T = m∠Q ⇒ because it is given

Step 3: SR ≅ RS ⇒ because of reflexive property (common side)

Step 4: Δ TSR ≅ ΔQRS ⇒ because of the AAS congruence theorem  

* The answer is number (2)

4 0
3 years ago
Read 2 more answers
Other questions:
  • Factor 18p-3618p−3618, p, minus, 36 to identify the equivalent expressions. Choose 2 answers: Choose 2 answers:
    8·2 answers
  • A case of grapefruit weighs 35 3/4 pounds. of this weight, 1/8 is not ripe. What is the weight of the grapefruit that are ripe?
    6·1 answer
  • What is the area of the hexagon below?<br> 12 m 2<br> 18 in 2<br> 24 in 2<br> 48 in 2
    6·2 answers
  • Given the arithmetic sequence an = 2 − 3(n − 1), what is the domain for n?
    10·2 answers
  • Seth ships 12 boxes with 16 blankets in each box how many blankets did Seth ship?
    8·1 answer
  • Find the area, and round to the nearest tenth
    11·1 answer
  • Why are handcuffs like souvenirs
    9·2 answers
  • Need help on this question and no the answer is not 21 I tried it
    11·2 answers
  • Can somebody please help me
    6·1 answer
  • In​ 2014, the population of a state was approximately 1,624,000. If the population decrease was about 0.59​%, find the populatio
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!