what are the following angles for triangle with hypotenuse and adjacent with rig

Question

what are the following angles for triangle with hypotenuse and adjacent with right angle with alpha degree and opposite side is a with beta degree between a and c.

1. beta =36, c=54, what is a

2. c=26, a=15, what is alpha?

3. c=5, b=3, what is a?

4. b=10m a=20 and what is beta?

5. alpha is 60, b=24, what is a?

6. beta is 5, c= 10, what is a?

7. a=25, b=36, c=what

8. c=14, b=12, what is alpha?

9. beta is 44, a=22, what is b

c is hypotenuse, a is the opposite side, and b is the adjacent side. the beta degree is at the top and the alpha degree is between c and b. please help.

Explanation / Answer

1) beta=36 ,c=54

then alpha=(180-90-36)=54

so sin(alpha)=sin(54)=a/c

=>.809016=a/54

=>a= 43.6869

2) c=26, a=15

in right angle: c^2=a^2+b^2

b^2=(26*26)-(15*15)

b^2=451

b=21.236

3)similarly: a^2=c^2-b^2

a^2=(5*5)-(3*3)

a^2=16

a=4

4)b=10 and a=20

then from the traingle tan(beta)=b/a

tan(beta)=10/20

beta=arctan(1/2)

beta= 26.565

5)alpha=60, b=24

then tan(alpha)=a/b

tan(60)= a/24

1.732*24=a

a=41.569

6)beta=5, c=10

from the traingle cos(beta)=a/c

cos(5)=a/10

0.9961*10=a

a=9.961

7)a=25, b=36

as discussed above : c^2=a^2+b^2

c^2=(25*25)+(36*36)

c^2=625+1296

c^2=1921

c=43.823

8)c=14, b=12   

from the traingle: cos(alpha)=b/c

cos(alpha)=12/14

alpha=arccos(.8571)

alpha=0.9998

9)beta=44,a=22

then tan(beta)=b/a

tan(44)=b/22

0.9656*22=b

b=21.245

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