SOLUTION: I have a right triangle, triangle ABC. Angle A is 70 degrees, angle B is 20 degrees and obviously, Angle C is 90. The length of side AB, or the opposite side is 183 miles. The leng

Algebra ->  Triangles -> SOLUTION: I have a right triangle, triangle ABC. Angle A is 70 degrees, angle B is 20 degrees and obviously, Angle C is 90. The length of side AB, or the opposite side is 183 miles. The leng      Log On


   

Question 370114: I have a right triangle, triangle ABC. Angle A is 70 degrees, angle B is 20 degrees and obviously, Angle C is 90. The length of side AB, or the opposite side is 183 miles. The length of side CB, or the base, is 172. What is the third side's length?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If C is the right angle then AB is the hypotenuse. With two sides of a right triangle we can use the Pythagorean Theorem to find the third side:
%28183%29%5E2+=+%28172%29%5E2+%2B+%28AC%29%5E2
Simplifying we get:
33489+=+29584+%2B+%28AC%29%5E2
Subtracting 29584 from each side we get:
3905+=+%28AC%29%5E2
Finding the square root of each side (and discarding the negative square root because sides of triangles cannot be negative):
sqrt%283905%29+=+sqrt%28%28AC%29%5E2%29
sqrt%283905%29+=+AC
which is the exact answer. Use your calculator on the square root to find a decimal approximation.