SOLUTION: Can you please take the time to help me solve this problem: In a right triangle, the length of the hypotenuse is 5 and the length of one of the legs is 3, determine the tangents of

Algebra ->  Angles -> SOLUTION: Can you please take the time to help me solve this problem: In a right triangle, the length of the hypotenuse is 5 and the length of one of the legs is 3, determine the tangents of      Log On


   

Question 99246: Can you please take the time to help me solve this problem: In a right triangle, the length of the hypotenuse is 5 and the length of one of the legs is 3, determine the tangents off all three angles. I would be really appreciate it if you did help me.
Thanks
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First, find the lengths of all the sides
(hypotenuse)2 = (side1)2 + (side2)2
5%2A2+=+3%2A2+%2B+x%2A2
x%2A2+=+5%2A2+-+3%2A2
x%2A2+=+25+-+9
x%2A2+=+16
x+=+4
It's what is known as a 3-4-5 triangle
The tangent function in trig is (opposite side) / (adjacent side)
For the angle opposite the length 3 side, call it A
Tan A = 3/4
For the angle opposite the length 4 side, call it B
Tan B = 4/3
The remaining angle, opposite the hypotenuse is 90 degrees, as
with any right triangle. Call it C
Tan C = Tan 90
Tan 90 = infinity. This is because the adjacent side is zero
and the reciprocal of zero is infinity. You need to plot it on
the unit circle to see this.