Maths-
General
Easy

Question

The angles of a triangle are in the ratio 3:5:10. Then ratio of smallest to greatest side is

  1. 1 colon sin space 10 to the power of ring operator
  2. 1 colon 2 sin space 10 to the power of 6
  3. 1 colon cos space 10 to the power of ring operator
  4. 1 colon 2 cos space 10 to the power of ring operator

hintHint:

The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.

The correct answer is: 1 colon 2 cos space 10 to the power of ring operator


    T h e space a n g l e s space o f space t h e space t r i a n g l e space A B C space a r e space d e n o t e d space b y space A comma space B comma space C space a n d space t h e space c o r r e s p o n d i n g space o p p o s i t e space s i d e s space b y space a comma space b comma space c.
s o space W e space k n o w space t h a t comma space
fraction numerator a over denominator sin space A end fraction space equals space fraction numerator b over denominator sin space B end fraction space equals space fraction numerator c over denominator sin space C end fraction space equals 2 R

    The angles of a triangle are in the ratio 3:5:10.

    sin A space colon space sin B space colon space sin C space equals space 3 space colon space 5 space colon space 10
space fraction numerator a over denominator 2 R end fraction space colon space fraction numerator b over denominator 2 R end fraction space colon space fraction numerator c over denominator 2 R end fraction space equals space 3 space colon space 5 space colon space 10 space space space space space space space space space space space space space space space space space space space space left curly bracket space space S o space L e t s space 3 x space plus space 5 x space plus space 10 space x space equals space 180 degree space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 18 x space equals 180 degree space space rightwards double arrow x space equals space 10 degree space space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space S o comma space space A equals space 30 degree space space B space equals space 50 degree comma space space C space equals space 100 degree space space right curly bracket
space left curly bracket space fraction numerator a over denominator 2 R end fraction equals 3 semicolon space fraction numerator b over denominator 2 R end fraction equals 5 semicolon space fraction numerator c over denominator 2 R end fraction equals 10 space right curly bracket
space space a equals 6 R semicolon space b equals 10 R semicolon space c equals 20 R space
    If a triangle has sides a, b, and c, then ratio of smallest to greatest side is
    According to question,
    Then ratio of smallest to greatest side is
    fraction numerator a space over denominator c end fraction equals fraction numerator sin space 30 degree over denominator sin space 100 degree end fraction space equals space fraction numerator 1 over denominator 2 space cross times space cos space 10 degree end fraction space space
left curly bracket space b c z space o f space a n g l e space C space i s space g r e a t e s t comma space c space s i d e space i s space g r e a t e r space t h a n space o t h r e s space divided by divided by space a n g l e space A space i s space s m a l l e s t comma space a space s i d e space i s space s m a l l e r space t h a n space o t h r e s space right curly bracket
fraction numerator 6 R over denominator 20 R end fraction space equals space fraction numerator 3 R over denominator 10 R end fraction space equals 3 over 10 space equals space fraction numerator 1 over denominator 2 space cross times space cos space 10 degree end fraction

    A triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c.

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