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
labwork [276]
2 years ago
12

two sides and an angle are given below. determine whether the given information results in one triangle, two triangles, or no tr

iangle at all. solve any resulting triangle(s). b = 8, c= 7, b = 170°

Mathematics
1 answer:
Verdich [7]2 years ago
8 0

Answer:

  A. single triangle. C = 8.74°, A = 1.26°, a = 1.01

Step-by-step explanation:

When two sides and an angle are given, the possibility of two (or zero) triangles exists only when the given angle is opposite the shorter of the two given sides. That is not the case here, so the given measures define one unique triangle.

<h3>Law of Sines</h3>

The law of sines tells us the sides and angles have the relation ...

  sin(A)/a = sin(B)/b = sin(C)/c

We can use this first to find angle C:

  sin(C) = c/b·sin(B)

  C = arcsin(c/b·sin(B)) = arcsin(7/8·sin(170°)) ≈ 8.7394°

  ∠C ≈ 8.74°

<h3>Remaining measures</h3>

Now that we know two angles, we can find the third:

  A = 180° -B -C = 180° -170° -8.74° = 1.26°

  ∠A = 1.26°

Using the law of sines again, we can find the measure of side 'a'.

  a = b·sin(A)/sin(B) = 8·sin(1.26°)/sin(170°) ≈ 1.01346

The measure of segment 'a' is about 1.01 units.

__

<em>Additional comment</em>

If 'a', 'b', and angle A are given, there will be zero triangles if b/a·sin(A) > 1. If b/a·sin(A) < 1 and b > a, there will be two (2) triangles. Otherwise, as here, there will be one unique triangle.

You might be interested in
PLEASE HELP!!! WILL AWARD BRAINLIEST!!! you work a part-time job earning 6.80/hr with tips that average 2.30/hr you work 20 hr/w
solmaris [256]
143.7  I believe since you take 6.80*20=136+46=2.3*20

136+46=182

182*7.65%=168.08

168.08*8.95%=153.04

153.04*6.1%=143.7
4 0
3 years ago
Read 2 more answers
Isabel works for 6 hours preparing for the art fair. She spends 3 hours on a sculpture and then paints 27 picture frames. How mu
Alecsey [184]

Answer: 3?

Step-by-step explanation: 3?

WOOOAH -_-

8 0
3 years ago
Which number has a 3 with a value that is 100 times greater than the value of 3 in 20.342 ?
Elodia [21]

Answer:

You didnt give any options, but I'm guessing one of them has a 3 in the tens digits, which should be the right answer.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
If lim(x-&gt;3) f(x)=7, which of the following must be true?
fenix001 [56]
<span>If lim(x->3) f(x)=7, then </span><span>f(3) = 7.</span>
5 0
3 years ago
Soo I need help... can u help?
Luda [366]

Answer:

I think its (6042 = 1780 + a) but I'm not really sure though but I hope if that helped somehow

6 0
3 years ago
Read 2 more answers
Other questions:
  • How much of his allowance did Nathan spend? Explain how you found your answer. WILL GIVE BRAINLIEST
    9·1 answer
  • The circumference of a circle is 20π cm. What is the DIAMETER of the circle?
    11·1 answer
  • Find the value of 8.3 × 24.2 × 0.03. Round your answer to the nearest hundredth.
    15·1 answer
  • What number - 5 = 14
    8·2 answers
  • Resources Complete each of the definitions with the appropriate phrase. Precision means that measurements are close to measureme
    13·1 answer
  • Jenna flipped a coin 375 times. It landed tails up 300 times. What is the experimental probability of a flip resulting in tails
    9·1 answer
  • How would you graph y=2x +5?
    9·2 answers
  • Solve for x and y<br><br><br><br> Please help!!!
    15·1 answer
  • I need the answer please
    7·1 answer
  • A machine can wrap 900 lollipops in 36 minutes what is the unit rate or lollipops wrapped every minute
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!