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Alex
2 years ago
14

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

Mathematics
1 answer:
Sliva [168]2 years ago
6 0

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

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