Question

if triangle ABC ~ triangle DEF and angle A = 55° , angle E = 77° then find the measure of angle C​

Answer 1

Answer:

Using the identity that: sin(3θ)=3sinθ−4sin

3

θ

The equation can be written as:

sin(3x)=k

As A and B are both solutions:

sin(3A)=sin(3B)

As A



=B, the other solution is given by:

3A=π−3B⟹A+B=

3

π

As A,B,C are angles of the same triangle:

A+B+C=π⟹C=π−(A+B)=π−

3

π

=

3

2π