Triangles And Properties Of Triangle Question 31
Question: Consider the following statements:
- There exists no triangle ABC for which $ \sin A+\sin B=\sin C. $
- If the angle of a triangle are in the ratio $ 1:2:3, $ Then its sides will be in the ratio $ 1:\sqrt{3}:2. $ Which of the above statements is/are correct?
Options:
A) 1 only
B) 2 only
C) Both 1 and 2
D) Neither 1 nor 2
Show Answer
Answer:
Correct Answer: C
Solution:
[c] 1. Given, $ \sin A+\sin B=\sin C $ $ a+b=c $ $ ( \because By\sin e,law,\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{sinC}{c}=K ) $ Here, the sum of two sides of $ \Delta ABC $ is equal to the third side, but it is not possible (Because by triangle inequality, the sum of the length of two sides of a triangle is always greater than the length of the third side) $ $ 2. Ratio of angles of a triangle $ A:B:C=1:2:3 $ $ A+B+C=180{}^\circ $
$ \therefore A=30{}^\circ $ $ B=60{}^\circ $ $ C=90{}^\circ $ the ratio in sides according to sine rule $ a:b:c=\sin A:\sin B:sinC $ $ =\sin 30{}^\circ :\sin 60{}^\circ :\sin 90{}^\circ $ $ =\frac{1}{2},\frac{\sqrt{3}}{2},1=\frac{1}{2}:\frac{\sqrt{3}}{2}:1 $
BETA
