Answer:
- a = 13 ft
- b = 16 ft
- c = 21 ft
- A = 39°
- B = 51°
Explanation:
You want the complete solution (side lengths and angles) for a right triangle with leg lengths a=13 ft and b=16 ft.
Solution
Since the two leg lengths are given, it is convenient to use the inverse tangent relation to find one of the acute angles.
Tan = Opposite/Adjacent
tan(A) = a/b
A = arctan(13/16) ≈ 39°
B = 90° -A = 51°
The hypotenuse can be found using the Pythagorean theorem, or it can be found using trigonometry. We have just computed angle A, so we can use that value to find the hypotenuse of the triangle.
Cos = Adjacent/Hypotenuse
Hypotenuse = Adjacent/Cos
c = b/cos(A) = 16/cos(39.093859°) ≈ 21 . . . . feet
Then the solution is ...
- a = 13 ft
- b = 16 ft
- c = 21 ft
- A = 39°
- B = 51°
__
Additional comment
Note the calculator is set to DEG mode so the angles are reported in degrees.
The hypotenuse is found using the original full-precision value of the angle, not the rounded value required to answer the problem statement.