SOLUTION: solve the right triangle. drawing the figure may help. 1.) B = 75 degree, a = 68 2.) b = 42, c = 80 3.) B = 15 degree, b = 52 4.) A = 75 degree, a = 126

Algebra ->  Trigonometry-basics -> SOLUTION: solve the right triangle. drawing the figure may help. 1.) B = 75 degree, a = 68 2.) b = 42, c = 80 3.) B = 15 degree, b = 52 4.) A = 75 degree, a = 126       Log On


   

Question 928855: solve the right triangle. drawing the figure may help.
1.) B = 75 degree, a = 68
2.) b = 42, c = 80
3.) B = 15 degree, b = 52
4.) A = 75 degree, a = 126
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1.
a=68, B=75° => A=90-75=15
to find side c we can use the definition:
cos%28angle%29=+adjacent_+leg%2Fhypotenuse

In this case we have:
cos%28beta%29=a%2Fc
After substituting beta=75° and a=68 we have:
cos%2875%29=68%2Fc
c=68%2Fcos%2875%29
c=68%2F0.2588
c=262.73
then b%5E2=c%5E2-a%5E2
b%5E2=262.73%5E2-68%5E2
b%5E2=69027-4624
b%5E2=64403
b=253.78

2.
b+=+42, c+=+80
c%5E2=a%5E2%2Bb%5E2
a%5E2=c%5E2-b%5E2
a%5E2=80%5E2-42%5E2
a%5E2=6400-1764
a%5E2=4636
a=68.09

3. B+=+15 degree, b+=+52
To find side a we can use the definition:
tan%28angle%29=opposite_leg%2Fadjacent_leg
In this case we have:
tan%28beta%29=b%2Fa
After substituting beta=15° and b=52 we have:
tan%2815%29=52%2Fa
a=52%2Ftan%2815%29
a=52%2F0.2679
a=194.07
now we can find c
c%5E2=a%5E2%2Bb%5E2
c%5E2=%28194.07%29%5E2%2B52%5E2
c%5E2=37663%2B2704
c%5E2=40367
c=200.9



4. A+=+75 degree, a+=+126
to find side b use :
tan%28alpha%29=a%2Fb
tan%2875%29=126%2Fb
b=126%2Ftan%2875%29
b=126%2F3.73
b=33.8
now find c:
c%5E2=a%5E2%2Bb%5E2
c%5E2=126%5E2%2B%2833.8%29%5E2
c%5E2=15876%2B1142.44
c%5E2=17018.44
c=130.5