SOLUTION: A triangle has a hypotenuse of 36 inches, it has a right angle opposite the hypotenuse, and a 20 degree angle, and a 70 degree angle. What is the length of the other two sides?

Algebra ->  Triangles -> SOLUTION: A triangle has a hypotenuse of 36 inches, it has a right angle opposite the hypotenuse, and a 20 degree angle, and a 70 degree angle. What is the length of the other two sides?       Log On


   

Question 239830: A triangle has a hypotenuse of 36 inches, it has a right angle opposite the hypotenuse, and a 20 degree angle, and a 70 degree angle.
What is the length of the other two sides?
So basically, a2 + b2 = 1296

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A triangle has a hypotenuse of 36 inches, it has a right angle opposite the hypotenuse, and a 20 degree angle, and a 70 degree angle.
What is the length of the other two sides?
So basically, a2 + b2 = 1296
:
What you say is true but both legs are unknown, but they give the angles, so you can use the sine or cosine
:
Sin = %28side+opposite%29%2Fhypotenuse
:
Find the side opposite the 20 degree angle; let it = a
sin(20) = a%2F36
.342 = a%2F36
a = .342 * 36
a = 12.31 inches
:
Now you can find the 2nd leg using pythag, or you can use the cosine
which %28side+adjacent%29%2Fhypotenuse
cos(20) = b%2F36
.940 = b%2F36
b = .940 * 36
b = 33.83 inches
;
:
We can check this using pythag
12.31^2 + 33.83^2 = 1296