Question

a triangle has sides 8cm and 5cm and an angle of 90 degree between them.calculate the smallest angle of the triangle ​

Answer 1

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;

$Tan\ x = \frac{Opposite}{Adjacent}$

$Tan\ x = \frac{5}{8}$

$Tan\ x = 0.625$

Take arctan of both sides

$x = tan^{-1}0.625$

$x = 32.0053832081$

$x = 32$ (Approximated)

Scenario 2 (Calculating y)

Let opposite = 8 cm

Let adjacent = 5 cm

In trigonometry, The relationship between opposite and adjacent is Tangent;

$Tan\ y = \frac{Opposite}{Adjacent}$

$Tan\ y = \frac{8}{5}$

$Tan\ y = 1.6$

Take arctan of both sides

$y = tan^{-1}1.6$

$y = 57.9946167919$

$y = 58$ (Approximated)

By comparing the angles, the smallest angle is 32 degrees