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

Hint:

In the given triangle the ratio of the angles is given so we will find the value of angles using the sum of angles of a triangle. Now we have the smallest and the largest angle and we know that the side opposite to the angles are smallest and largest side respectively. At last, by using sine formula, we can find the ratio of the smallest and largest side

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


    I n space triangle A B C space comma r a t i o space o f space angle A colon angle B colon angle C equals space 3 colon 5 colon 10
S o comma space angle A equals space 3 x comma space angle B equals 5 x comma space angle C equals space 10 x
w e space k n o w space t h a t space angle A plus angle B plus angle C equals 180 degree
rightwards double arrow 3 x plus 5 x plus 10 x equals 180 degree
rightwards double arrow 18 x equals 180 degree
rightwards double arrow x equals 10 degree
S o comma space angle A equals 30 degree comma space angle B equals 50 degree comma space angle C equals 100 degree
A s space angle C space i s space t h e space g r e a t e s t space a n g l e comma space s o space t h e space s i d e space o p p o s i t e space t o space i t space i. e comma space c space i s space t h e space l a r g e s t space s i d e.
A s space angle A space i s space t h e space s m a l l e s t space a n g l e comma space s o space t h e space s i d e space o p p o s i t e space t o space i t space i. e comma space a space i s space t h e space s m a l l e s t space s i d e.
I n space triangle A B C comma space
u sin g space sin e space f o r m u l a comma
fraction numerator a over denominator S i n A end fraction equals fraction numerator b over denominator S i n B end fraction equals fraction numerator c over denominator S i n C end fraction
rightwards double arrow fraction numerator a over denominator sin space A end fraction equals fraction numerator c over denominator sin space C end fraction
rightwards double arrow a over c equals fraction numerator sin space A over denominator sin space C end fraction
space space space space space space space space space space equals fraction numerator sin space 30 degree over denominator sin 100 degree end fraction
space space space space space space space space space equals fraction numerator sin space 30 degree over denominator sin space left parenthesis 90 space plus 10 right parenthesis degree end fraction
space space space space space space space space space equals fraction numerator begin display style 1 half end style over denominator cos space 10 degree end fraction
space space space space space space space space equals fraction numerator 1 over denominator 2 cos space 10 degree end fraction
a colon c equals 1 colon 2 cos space 10 degree

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