SOLUTION: In this problem I need help with finding two sides of a right triangle. One of the sides is a leg and another is the hypotenuse. I have one leg which is 8. I have the 3 degrees t

Algebra ->  Triangles -> SOLUTION: In this problem I need help with finding two sides of a right triangle. One of the sides is a leg and another is the hypotenuse. I have one leg which is 8. I have the 3 degrees t      Log On


   

Question 837932: In this problem I need help with finding two sides of a right triangle. One of the sides is a leg and another is the hypotenuse. I have one leg which is 8. I have the 3 degrees too which is 90 degrees, 67, and 23.
I was thinking maybe it had something to do with the Pythagorean therom. But I would need 2 sides. So that would not work.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the only length you have is the length of one leg, but you know the measures of the angles, you need to use the trigonometric ratios:
tangent=opposite_side%2Fadjacent_side
cosine=adjacent_side%2Fhypotenuse

Where is the side with length 8?
Is it adjacent to the 23%5Eo angle or to the 67%5Eo angle?

ADJACENT TO THE 23%5Eo ANGLE:
tan%2823%5Eo%29=leg%2F8 and cos%2823%5Eo%29=8%2Fh
tan%2823%5Eo%29=0.424475 (rounded) and cos%2823%5Eo%29=0.920505 (rounded)
tan%2823%5Eo%29=leg%2F8 --> leg=8%2Atan%2823%5Eo%29=3.40 (rounded)
cos%2823%5Eo%29=8%2Fh --> h=8%2Fcos%2823%5Eo%29=8.69 (rounded)

ADJACENT TO THE 67%5Eo ANGLE:
tan%2867%5Eo%29=leg%2F8 and cos%2867%5Eo%29=8%2Fh
tan%2867%5Eo%29=2.355852 (rounded) and cos%2867%5Eo%29=0.390731 (rounded)
tan%2867%5Eo%29=leg%2F8 --> leg=8%2Atan%2867%5Eo%29=18.85 (rounded)
cos%2867%5Eo%29=8%2Fh --> h=8%2Fcos%2867%5Eo%29=20.47 (rounded)