Question

In order to apply the law of sines to find the length of the side of a triangle, it is enough to know which of the following?

A. Two angles and a side
B. All three angles
C. Two sides and one angle
D. The area of the triangle ...?

Answer 1

We must have two angles and a side.

A is the correct option.

Explanation:

For any triangle ABC, the law of sine is given by

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

From this formula it is clear that in order to find the length of the side of the triangle, we must have two angles and a side.

Let us understand this by assuming that we need to find a (length of the side). From the formula, we have

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

Thus, to find the length a, we must have b, sin A and sin B.

Hence, o find the length of the side of the triangle, we must have two angles and a side.

Answer 2

A. Two angles and a side
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any shaped triangle to the sines of its angles.