Is 2cubed an integer?

Determine the number of possible solutions for a triangle with B=37 degrees, a=32, b=27

vladimir1956 [14]

Answer:

Two possible solutions

Step-by-step explanation:

we know that

Applying the law of sines

$\frac{a}{sin(A)}=\frac{b}{Sin(B)}=\frac{c}{Sin(C)}$

we have

$a=32\ units$

$b=27\ units$

$B=37\°$

step 1

Find the measure of angle A

$\frac{a}{sin(A)}=\frac{b}{Sin(B)}$

substitute the values

$\frac{32}{sin(A)}=\frac{27}{Sin(37\°)}$

$sin(A)=(32)Sin(37\°)/27=0.71326$

$A=arcsin(0.71326)=45.5\°$

The measure of angle A could have two measures

the first measure-------> $A=45.5\°$

the second measure -----> $A=180\°-45.5\°=134.5\°$

step 2

Find the first measure of angle C

Remember that the sum of the internal angles of a triangle must be equal to $180\°$

$A+B+C=180\°$

substitute the values

$A=45.5\°$

$B=37\°$

$45.5\°+37\°+C=180\°$

$C=180\°-(45.5\°+37\°)=97.5\°$

step 3

Find the first length of side c

$\frac{a}{sin(A)}=\frac{c}{Sin(C)}$

substitute the values

$\frac{32}{sin(37\°)}=\frac{c}{Sin(97.5\°)}$

$c=Sin(97.5\°)\frac{32}{sin(37\°)}=52.7\ units$

therefore

the measures for the first solution of the triangle are

$A=45.5\°$ , $a=32\ units$

$B=37\°$ , $b=27\ units$

$C=97.5\°$ , $b=52.7\ units$

step 4

Find the second measure of angle C with the second measure of angle A

Remember that the sum of the internal angles of a triangle must be equal to $180\°$

$A+B+C=180\°$

substitute the values

$A=134.5\°$

$B=37\°$

$134.5\°+37\°+C=180\°$

$C=180\°-(134.5\°+37\°)=8.5\°$

step 5

Find the second length of side c

$\frac{a}{sin(A)}=\frac{c}{Sin(C)}$

substitute the values

$\frac{32}{sin(37\°)}=\frac{c}{Sin(8.5\°)}$

$c=Sin(8.5\°)\frac{32}{sin(37\°)}=7.9\ units$

therefore

the measures for the second solution of the triangle are

$A=45.5\°$ , $a=32\ units$

$B=37\°$ , $b=27\ units$

$C=8.5\°$ , $b=7.9\ units$

6 0

3 years ago

300 school children went on a field trip. 30% of them were first graders, 45% second graders and the rest were third graders. Ho

mrs_skeptik [129]

Answer:

just take 45 and 30 percent add them to get 75% so find 75 percent of 300 then subtract it and you get 75

Step-by-step explanation:

3 0

3 years ago

Matt claims that the decimal 6.25 is equivalent to the fraction 25/4. Explain how that's incorrect.

sdas [7]

Actually, that is a trick question. Matt is correct because 24/4 is equal to 6. 1/4 is equal to 0.25. Add them together and you get 6.25. I just split 25/4 into 24/4 and 1/4 if you didn't understand what I did.

4 0

4 years ago

Read 2 more answers

A student takes an 18-question, multiple-choice exam with five choices for each question and guesses on each question. Assume th

Kobotan [32]

Answer:

Probability of getting at least 9 out of 18 correctly is 0.0043

Step-by-step explanation:

We have

n = 18

p = 1/5 for correct answer

q = 4/5 for wrong answer

P( 9 $\leq$ X $\leq$ 18) = 1 - P(0 $\leq$ X $\leq$ 8)

= 1 - 0.9957

=0.0043

7 0

3 years ago

¿Cuál propiedad de los números complejos se muestra a continuación?

Semenov [28]

Answer:

D) Comutativa

Step-by-step explanation:

a+b=b+a (álgebra)

espero que te sirva mi ayuda

5 0

3 years ago