In triangle ABC, angle A=47° , angle B=73° and side B=14.6cm . find the length of side A ?

Answer 1

To find the length of side A, we can use the Law of Sines. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In this case, we have the length of side B (14.6 cm) and the measure of angle B (73°). We want to find the length of side A, which is opposite to angle A (47°).

Let's set up the equation using the Law of Sines:

(sin A) / a = (sin B) / b

Plugging in the values we know:

(sin 47°) / a = (sin 73°) / 14.6 cm

Now, to solve for a, we can cross-multiply and divide:

a = (14.6 cm) * (sin 47°) / (sin 73°)

Using a calculator, we can find:

a ≈ 11.116 cm

Therefore, the length of side A is approximately 11.116 cm.