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# Triangle Problem | PRMO-2018 | Problem No-24

Try this beautiful Trigonometry Problem based on Triangle from PRMO -2018, Problem 24.

## Triangle Problem - PRMO 2018- Problem 24

If is the number of triangles of different shapes (i.e. not similar) whose angles are all integers (in degrees), what is ?

,

Trigonometry

Triangle

Integer

## Suggested Book | Source | Answer

Pre College Mathematics

#### Source of the problem

Prmo-2018, Problem-24

## Try with Hints

#### First Hint

Given that is the number of triangles of different shapes. Therefore the different shapes of triangle the angles will be change . at first we have to find out the posssible orders of the angles that the shape of the triangle will be different...

Now can you finish the problem?

#### Second Hint

case 1 : when &

Case 2 : When two angles are same

1,1,178
2,2,176

89,89,2

#### Solution

But we have one case

Such type of triangle
When 3 angles are same
So all distinct angles's triangles

Now, distinct triangle

## Subscribe to Cheenta at Youtube

Try this beautiful Trigonometry Problem based on Triangle from PRMO -2018, Problem 24.

## Triangle Problem - PRMO 2018- Problem 24

If is the number of triangles of different shapes (i.e. not similar) whose angles are all integers (in degrees), what is ?

,

Trigonometry

Triangle

Integer

## Suggested Book | Source | Answer

Pre College Mathematics

#### Source of the problem

Prmo-2018, Problem-24

## Try with Hints

#### First Hint

Given that is the number of triangles of different shapes. Therefore the different shapes of triangle the angles will be change . at first we have to find out the posssible orders of the angles that the shape of the triangle will be different...

Now can you finish the problem?

#### Second Hint

case 1 : when &

Case 2 : When two angles are same

1,1,178
2,2,176

89,89,2

#### Solution

But we have one case

Such type of triangle
When 3 angles are same
So all distinct angles's triangles

Now, distinct triangle

## Subscribe to Cheenta at Youtube

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