SOLUTION: sketch figure and solve each right triangle ABC with right angle at C. give that. 1. A=15° and c=37? 2. B=64° and c=19.2? 3. A=15° and c=25? 4. A=45° and c=16 5. B

Algebra ->  Trigonometry-basics -> SOLUTION: sketch figure and solve each right triangle ABC with right angle at C. give that. 1. A=15° and c=37? 2. B=64° and c=19.2? 3. A=15° and c=25? 4. A=45° and c=16 5. B      Log On


   



Question 955991: sketch figure and solve each right triangle ABC with right angle at C.
give that.
1. A=15° and c=37?
2. B=64° and c=19.2?
3. A=15° and c=25?
4. A=45° and c=16
5. B=56° and c=16
please give me answer with solve and figure thanks :)

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!



1. A=15° and c=37
To find side a we can use the definition:
sin%28alpha%29=opposite+%2Fhypotenuse
In this case we have:
sin%28alpha%29=a%2Fc
After substituting alpha=15 and c=37 we have:
sin%2815%29=a%2F37
a=37%2Asin%2815%29
a=37%2A0.2588
a=9.5763
a=9.58
now we can use Pythagoras theorem to find b
c%5E2=a%5E2%2Bb%5E2
b%5E2=c%5E2-a%5E2
b%5E2=37%5E2-%289.58%29%5E2
b%5E2=1369-91.7764
b%5E2=1277.2236
b=sqrt%281277.2236%29
b=35.74

2. B=64° and c=19.2?
In this case we have:
sin%28beta%29=b%2Fc
After substituting beta=64 and c=19.2 we have:
sin%2864%29=b%2F19.2
b=19.2%2Asin%2864%29
b=19.2%2A0.8988
b=17.26
c%5E2=a%5E2%2Bb%5E2
a%5E2=c%5E2-b%5E2
a%5E2=%2819.2%29%5E2-%2817.26%29%5E2
a%5E2=368.64-297.9076
a%5E2=70.7324
a=sqrt%2870.7324%29
a=8.41

3. A=15° and c=25?
sin%28alpha%29=a%2Fc
After substituting alpha=15 and c=25 we have:
sin%2815%29=a%2F25
a=25%2Asin%2815%29
a=25%2A0.2588
a=6.47

now we can use Pythagoras theorem to find b
c%5E2=a%5E2%2Bb%5E2
b%5E2=c%5E2-a%5E2
b%5E2=25%5E2-%286.47%29%5E2
b%5E2=625-41.8609
b%5E2=583.1391
b=sqrt%28583.1391%29
b=24.15

4. A=45° and c=16
sin%28alpha%29=a%2Fc
After substituting alpha=45 and c=16 we have:
sin%2845%29=a%2F16
a=16%2Asin%2845%29
a=16%2A%28sqrt%282%29%2F2%29
a=8sqrt%282%29

now we can use Pythagoras theorem to find b
c%5E2=a%5E2%2Bb%5E2
b%5E2=c%5E2-a%5E2
b%5E2=16%5E2-%288sqrt%282%29%29%5E2
b%5E2=256-64%2A2
b%5E2=256-128
b%5E2=128
b=sqrt%28128%29
b=11.31

5. B=56° and c=16
sin%2856%29=b%2F16
b=16%2Asin%2856%29
b=16%2A0.829
b=13.26
c%5E2=a%5E2%2Bb%5E2
a%5E2=c%5E2-b%5E2
a%5E2=%2816%29%5E2-%2813.26%29%5E2
a%5E2=256-175.8276
a%5E2=80.1724
a=sqrt%2880.1724%29
a=8.95