Answer: 130.5 ft. ; 30 degrees
Explanation:
(1) Understand basic trig rules. You can solve this in either of two ways: use sine, or use cosine, to find the length of the hypotenuse of the given triangle.
- This is a 90 degree triangle where we are given two angles: 90 degrees and 40 degrees. 180 - 90 - 40 = 50 degrees as the other angle.
sin(50) = 100/x
cos(40) = 100/x
x = 100/sin(50)
OR
x = 100/cos(40)
Plug this into a calculator, ensuring it is in degrees mode.
x = 130.5 ft
(2) In this situation, use trig basics again:
cos(A) = 13/15 --> A = arccos(13/15) = 29.9 degrees or 30 degrees. The given hint in the problem is that angle A is the smallest.
CHECK:
We can check if our logic makes sense by ensuring A is a smaller angle than angle C: 180 - 90 - 30 = 60 degrees = Angle C. Angle C > Angle A.