SOLUTION: In Triangle ABC, A= 42 degrees, B= 68 degrees, and c= 15. Find the length of a and b

Algebra ->  Trigonometry-basics -> SOLUTION: In Triangle ABC, A= 42 degrees, B= 68 degrees, and c= 15. Find the length of a and b       Log On


   

Question 453480: In Triangle ABC, A= 42 degrees, B= 68 degrees, and c= 15. Find the length of a and b
Answer by pedjajov(51) About Me  (Show Source):
You can put this solution on YOUR website!
If we draw a height h from vertex C it divides side c in point D into two pieces x=AD and y=BD
:
Also it forms two right triangles:
- triangle ADC with one leg being height other one being x and b for hypotenuse
- triangle BDC with one leg being height other one being y and a for hypotenuse
:
We have for x, y and c:
x+y=c -> x+y=15 -> x=15-y
:
In triangle ADC we have tan%2842%29=h%2Fx -> h=x%2Atan%2842%29
In triangle BDC we have tan%2868%29=h%2Fy -> h=y%2Atan%2868%29
:
Now we have -> x%2Atan%2842%29=y%2Atan%2868%29
If we substitute x with x=15-y we have:
%2815-y%29%2Atan%2842%29=y%2Atan%2868%29
15%2Atan%2842%29-y%2Atan%2842%29=y%2Atan%2868%29
15%2Atan%2842%29=y%2Atan%2842%29%2By%2Atan%2868%29
y=15%2Atan%2842%29%2F%28tan%2842%29%2Btan%2868%29%29
:
From here:
x=15-y
x=15%2Atan%2868%29%2F%28tan%2842%29%2Btan%2868%29%29
:
Knowing x we can find b=AC:
cos%2842%29=x%2Fb
b=x%2Fcos%2842%29
b=15%2Atan%2868%29%2Fcos%2842%29%28tan%2842%29%2Btan%2868%29%29
:
b=14.80
:
Knowing y we can find c=BC:
cos%2868%29=y%2Fc
c=y%2Fcos%2868%29
c=15%2Atan%2842%29%2Fcos%2868%29%28tan%2842%29%2Btan%2868%29%29
:
c=10.68