Question

Use the triangle shown on the right to answer the question. According to the law on sines, which of the following statement(s) are true ? Check all that apply

Answer 1

Answer:

The statements which are true are:

• $a\sin B=b\sin A$

• $\dfrac{a}{\sin A}=\dfrac{b}{\sin B}$

• $\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

Step-by-step explanation:

In Trigonometry, the Law of Sine relates the length of sides of a triangle to the angle of a triangle.

According to this law if a,b and c are the sides of a triangle and A,B and C  respectively are opposite angles to the side.

Hence, we have:

$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

i.e. we have:

$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}$

This could also be given by:

$a\sin B=b\sin A$

$\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

Answer 2

Answer:

See below.

Step-by-step explanation:

The law of sines is usually written as a / sin A = b / sin b == c / sin C    where a is the side opposite angle A ,etc.

The first equation is true because it is obtained by cross multiplying

a / sin A = b / sin B,  therefore   b sin A = a sin B.

The second one is not true.

The third and fourth are both true.