Question

The angles 46 degrees and 44 degrees are complementary. True or False

Answer 1

1. Complementary angles are angles whose measures add up to 90°.
46° + 44° = 90°, so the angles are complementary. true

2. sin(x) = cos(90-x). Here's why:
Sine = opposite/hypotenuse
Cosine = adjacent/hypotenuse
The side opposite one angle is the same as the side adjacent to the opposite angle.
Therefore sin(angle) = cos(opposite angle)
These can be expressed as (x) and (90-x), as we will explore in question #3.
Anyways, sin(60°) = cos(90-60°) = cos(30°), so this is true

3. If we have a right triangle, it must have one right angle measuring 90°.
The angles of a triangle add up to 180°.
The other two angles' measures must add up to 90° because of this. true

4. true
Use the two sides to find the third (Pythagorean theorem)
Use the Law of Cosines to find each angle.

5. false
We need a side to know how large the triangle is going to be.
This is why triangles that share two angles are similar but not necessarily congruent.