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
Jobisdone [24]
3 years ago
14

Find b, given that a = 20, angle A = 30°, and angle B = 45° in triangle ABC

Mathematics
2 answers:
Kamila [148]3 years ago
6 0
<span>The side b is opposite to the angle B, applying the law of the sines, we have:

</span>\frac{a}{sinA} = \frac{b}{sinB}
\frac{20}{sin30^0} = \frac{b}{sin45^0}
\frac{20}{ \frac{1}{2} } = \frac{b}{ \frac{ \sqrt{2} }{2} }
20* \frac{ \sqrt{2} }{2}  = b* \frac{1}{2}
\frac{20 \sqrt{2} }{2} = \frac{b}{2}
2*b =2*20 \sqrt{2}
2b = 40 \sqrt{2}
b =  \frac{40 \sqrt{2} }{2}
\boxed{b = 20 \sqrt{2} }
Inga [223]3 years ago
4 0

Answer:

b = 20√2

Step-by-step explanation:

Given: ΔABC

           a = 20 , m∠A =  30° and m∠B = 45°

To find: value of b.

We use Sine result, which state that

\frac{a}{sin\,A}=\frac{b}{sin\,B}

Substituting given values we, get

\frac{20}{sin\,30^{\circ}}=\frac{b}{sin\,45^{\circ}}

we know that sin\,30^{\circ}=\frac{1}{2}\:and\:sin\,45^{\circ}=\frac{1}{\sqrt{2}}, we get

\frac{20}{\frac{1}{2}}=\frac{b}{\frac{1}{\sqrt{2}}}

20{\times2}=b\times\sqrt{2}

b\times\sqrt{2}=40

b=\frac{40}{\sqrt{2}}

b=20\sqrt{2}

Therefore, b = 20√2

You might be interested in
How do I make 9.076 turn into expandedform
Contact [7]

Answer:

9 + 0.0 + 0.07 + 0.006

Step-by-step explanation:

9 + 0.0 + 0.07 + 0.006

4 0
3 years ago
Solve each proportion.<br> 2/4=4/p-3<br>pls help​
eduard

Answer:

p=\frac{8}{7}

Step-by-step explanation:

\frac{2}{4} = \frac{4}{p} - 3

\frac{1}{2} = \frac{4}{p} - 3 (simplify)

\frac{1}{2}+3 = \frac{4}{p} - 3+3

\frac{1}{2}+3 = \frac{4}{p} (Add 3 to both sides)

\frac{7}{2}= \frac{4}{p} (simplify)

\frac{7}{2}p= \frac{4}{p}*p

\frac{7p}{2}=4 (Multiply both sides by p)

\frac{7p}{2}*2=4*2

7p=8 (Multiply both sides by 2)

\frac{7p}{7}=\frac{8}{7}

p=\frac{8}{7} (Divide both sides by 7)

7 0
3 years ago
Factor the expression 10y+6​
Sphinxa [80]

Answer:

2(5y+3)

Step-by-step explanation:

10y+6​

Factor out 2

2*5y + 2*3

2(5y+3)

7 0
3 years ago
Read 2 more answers
PLS HELP. It’s question 18
Gnom [1K]

Answer:

no

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
CAN SOMEONE PLEASE HELP
Inessa [10]

That Is The Correct answer ) 20

Hope I Helped

- Dante

5 0
3 years ago
Read 2 more answers
Other questions:
  • Denise has 5 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the
    5·1 answer
  • Determine the number of subsets of 3,4,5,6,7,8,9,10,11,12,13,14,15
    15·1 answer
  • How do you do two coulmn proofs in geometry ?
    15·1 answer
  • Titanium-44 is a radioactive isotope such that every 63 years, its mass decreases by half. For a sample of titanium-44 with an i
    12·1 answer
  • Simplify 3/4 and 6/7
    15·1 answer
  • Onvert the unit of weight. Enter your answer in the box.<br><br> 3/4 lb = <br> oz
    12·1 answer
  • A recipe that makes 10 raspberry muffins calls for / teaspoons of baking powder. How much baking powder is needed to make 3 doze
    12·2 answers
  • Help pls.. Fake answers will reported!...
    9·1 answer
  • If the area of a square is 49in2 what is one side length
    13·1 answer
  • Factorize of 2a³-a²+a-2​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!