Question
Download Solution PDFConsider the following statements:
1. There exists no triangle ABC for which sin A + sin B = sin C.
2. If the angles of a triangle are in the ratio 1 : 2 : 3, then its sides will be in the ratio 1 : √3 : 2.
Which of the above statements is/are correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Calculations:
Consider, a, b, c are the sides of triangle and A, B, C are the angles of the triangle.
We know that,
⇒
Given , sin A + sin B = sin C
⇒ A + B = C.
⇒ a + b = c
This is not posible.
Hence, there exists no triangle ABC for which sin A + sin B = sin C.
(2) Given, the angles of a triangle are in the ratio 1 : 2 : 3.
Consider the angles of a triangle are A = x, B = 2x and C = 3x.
We know that, Sum of the angles of the triangle is 180°
Hence, x + 2x + 3x = 180
6x = 180°
x = 30º
Angles are A = 30º, B = 60º and C = 90º
We know that,
Hence, the angles of a triangle are in the ratio 1 : 2 : 3, then its sides will be in the ratio 1 : √3 : 2..
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