SOLUTION: Solve for x. Round your answer to 2 decimal places. A right triangle is shown where the angle between the hypotenuse, of length x units, and a leg, of length eighteen units, is

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve for x. Round your answer to 2 decimal places. A right triangle is shown where the angle between the hypotenuse, of length x units, and a leg, of length eighteen units, is      Log On


   

Question 1106849: Solve for x. Round your answer to 2 decimal places.
A right triangle is shown where the angle between the hypotenuse, of length x units, and a leg, of length eighteen units, is fifty degrees.
Found 2 solutions by Boreal, addingup:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
18^2+y^2=x^2
we know that cosine of 50=18/x, using the adjacent leg
x=18/cos 50=28.00 ANSWER
The other leg^2 is 28^2-18^2=784-324=460 and the leg is 21.44

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
So we are solving for the length of the hypotenuse:
Short leg: 18
hypotenuse: x
angle (see picture below): 50 degrees
Since the acute angles in any right triangle are complementary (they add up to 90°):
other acute angle: 90-50 = 40
I'm going to use this second angle to get your answer:
csc(40) = hypotenuse/18
csc(40) * 18 = hypotenuse
1.556 * 18 = hypotenuse
hypotenuse = 28