Answer:
The smallest angle is 32 degrees
Step-by-step explanation:
The given parameters show that the triangle is a right angled triangle;
Let the two other angles be represented by x and y;
Since the angle between side 5 cm and side 8 cm is 90, we can represent any of this sides as the opposite and as the adjacent;
Scenario 1 (Calculating x)
Let opposite = 5 cm
Let adjacent = 8 cm
In trigonometry, The relationship between opposite and adjacent is Tangent;
[tex]Tan\ x = \frac{Opposite}{Adjacent}[/tex]
[tex]Tan\ x = \frac{5}{8}[/tex]
[tex]Tan\ x = 0.625[/tex]
Take arctan of both sides
[tex]x = tan^{-1}0.625[/tex]
[tex]x = 32.0053832081[/tex]
[tex]x = 32[/tex] (Approximated)
Scenario 2 (Calculating y)
Let opposite = 8 cm
Let adjacent = 5 cm
In trigonometry, The relationship between opposite and adjacent is Tangent;
[tex]Tan\ y = \frac{Opposite}{Adjacent}[/tex]
[tex]Tan\ y = \frac{8}{5}[/tex]
[tex]Tan\ y = 1.6[/tex]
Take arctan of both sides
[tex]y = tan^{-1}1.6[/tex]
[tex]y = 57.9946167919[/tex]
[tex]y = 58[/tex] (Approximated)
By comparing the angles, the smallest angle is 32 degrees
