SOLUTION: Hello, I am in Algebra 1(Integrated Algebra), as in the 9th grade class. We are doing right triangles and using Pythagorean Therom and ratios like tangent, sine, and cosine. I am c

Question 433691: Hello, I am in Algebra 1(Integrated Algebra), as in the 9th grade class. We are doing right triangles and using Pythagorean Therom and ratios like tangent, sine, and cosine. I am confused on the following problem:

The legs of a right triangle measure 54 and 33. Find to the nearest
degree the measure of the smallest angle of the triangle.
Is the 54 the hypotenuse or either the opposite or adjacent leg? And, which angle is the smallest? I know it is not the one that measures 90 degrees. Thank you so much for your time! I would greatly appreciate it if you could get back to me before tomorrow! Thanks again!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The legs of a right triangle measure 54 and 33.
Find to the nearest degree the measure of the smallest angle of the triangle.
:
Usually the "legs" refer to the sides that are not the hypotenuse
It will help to draw this out triangle ABC, where B is the right angle and b is the hypotenuse, then
a = 33
c = 54
:
find angle A, side opposite = 33, side adjacent = 54 (smallest angle has smallest side opposite (a)
:
tan(A) =
Find the arctan (tan^-1)
A = 31.43 degrees
:
We can confirm this is the smallest angle by finding C
180 - 90 - 33.429 = 58.57
:
Did this make sense to you now?
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