Question

The ratio of angle measures of triangle ABC is a : b:y=3: 2:13. Find>the length of the shortest side if a - b = 3.​

Answer 1

Given :- The ratio of angle measures of triangle ABC is a : b:y=3: 2:13. Find the length of the shortest side if a - b = 3

Answer :-

Let angles are 3x , 2x and 13x respectively .

so,

→ 3x + 2x + 13x = 180°

→ 18x = 180°

→ x = 10°

then,

→ a = 3x = 3 * 10 = 30°

→ b = 2x = 2 * 10° = 20°

→ y = 13x = 130°

then,

→ a/ sin a = b / sin b

→ a / sin 30° = b / sin 20°

→ sin 20° / sin 30° = b / a

→ sin 20° / sin 30° = b / (b + 3)

→ 2 * sin 20° = b / (b + 3)

→ 2 * 0.34 = b / (b + 3)

→ 0.68 * b + 2.04 = b

→ 2.04 = b - 0.68b

→ 2.04 = 0.32b

→ b = 6.375 (Ans.)

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Answer 2

Given : The ratio of angle measures of ABC is A  : B : C  = 3  : 2  :  13

a - b = 3

To Find : length of the shortest side

Solution:

A  : B : C  = 3  : 2  :  13

=> a = 3k  , b = 2k  ,  c = 13k

3k + 2k + 13k = 180°

=> 18k = 180°

=> k = 10°

=>  A = 3k  , B = 2k  ,  C = 13k

k = 10

=> A = 30  , B = 20  ,  C = 130

Shortest sides opposite to  B  is b

a/SinA  = b/SinB

=> a/Sin30°  = b/Sin20°

a - b = 3

=> a = b + 3

=> (b + 3)/Sin30°  =b/Sin20°

=>  2b + 6  =2.9238b

=>0.9238b = 6

=> b  = 6.49488

=> b  = 6.495

Shortest side  is  6.495  

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