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

The smallest angle is 32 degrees

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 = (Opposite)/(Adjacent)`

`Tan\ x = (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 = (Opposite)/(Adjacent)`

`Tan\ y = (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