In Making Connections, the **sine, cosine, and tangent are the same** for triangles with different side length and with **angles of 30, 60, and 45**. This is true based on the following definitions.

**DEFINITION**: Triangles with the same angles but different lengths are **similar** (same shape but different size) and produce the same ratio when certain sides are divided.

**DEFINITION**: Ratios of certain sides in two different triangles with the same angles are congruent (similarity ratios).

## Practice: Finding Missing Parts

- Find the missing parts of each triangle (angles and sides) using the Pythagorean Theorem, the Triangle Sum Principle, and special right triangle relationships.
- Then write the trig ratios. Leave your answers in fraction form (note, be sure to rationalize the denominator when applicable).

- \(\angle a=\)
- \(x=\)
- sin \(40^\circ\)=
- tan \(a=\)
- cos \(40^\circ\)=
- \(\angle b=\)
- \(y=\)
- \(z=\)
- sin \(30^\circ\)=
- tan \(b=\)
- cos \(30^\circ\)=