Question

Using the following triangle, write a proof to verify that sinA/a=sinC/c

Answer 1

Answer:

Proved: $c\sin A=a\sin C\Rightarrow \frac{\sin A}{a}=\frac{\sin C}{c}$

Step-by-step explanation:

Given: A triangle

To prove: $\frac{\sin A}{a}=\frac{\sin C}{c}$

Solution:

Trigonometry is a branch of mathematics that explains relationship between sides and angles of the triangle.

Sine of angle = side opposite to the angle / hypotenuse

In ΔADB,

$\sin A=\frac{BD}{AB}=\frac{h}{c}\\\Rightarrow h=c\sin A\,\,\,(i)$

In ΔBDC,

$\sin C=\frac{BD}{BC}=\frac{h}{a}\\\Rightarrow h=a\sin C\,\,\,(ii)$

From equations (i) and (ii),

$c\sin A=a\sin C\\\frac{\sin A}{a}=\frac{\sin C}{c}$

Hence proved