| 1. There exists no triangle ABC for which \[\sin A+\sin B=\sin C.\] |
| 2. 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? |
A) 1 only
B) 2 only
C) Both 1 and 2
D) Neither 1 nor 2
Correct Answer: C
Solution :
| [c] 1. Given, \[\sin A+\sin B=\sin C\] |
| \[a+b=c\] |
| \[\left( \because \,\,By\sin e\,law,\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\operatorname{sinC}}{c}=K \right)\] |
| 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 |
| \[a:b:c=\sin A:\sin B:\operatorname{sinC}\] |
| \[=\sin 30{}^\circ :\sin 60{}^\circ :\sin 90{}^\circ \] |
| \[=\frac{1}{2},\frac{\sqrt{3}}{2},1=\frac{1}{2}:\frac{\sqrt{3}}{2}:1\] |
You need to login to perform this action.
You will be redirected in
3 sec
