Introduction

Right triangles are everywhere! Without realizing it, you probably see right triangles and use their relationships each day. Right triangles are used to solve many real-world problems because they have many special relationships among their angles and sides. Need to find the distance from one point to another? You can use right triangle relationships. Want to know the angle of elevation from your location to the top of a mountain? You can use right triangle relationships. Want to find the angle between two sides of a figure? You can use right triangle relationships. Right triangles have many special properties that allow us to answer questions about the world around us!

Essential Questions

How do we define sine, cosine, and tangent?
How do we know when right triangles are similar?
What are the special relationships present in 45-45-90 and 30-60-90 triangles?
How are the sine and cosine of complementary angles related?
What is the Pythagorean Theorem and how can we use it to solve everyday problems?
How can we use trigonometric ratios to solve for missing parts in right triangles?

Key Terms

Hypotenuse - the longest side of a right triangle, across from the right angle

Opposite side - the side across from a given acute angle in a right triangle

Adjacent side - the side next to a given acute angle in a right triangle, that's not the hypotenuse

Sine - In a right triangle, the sine of an acute angle is the ratio of the opposite side/hypotenuse.

Cosine - In a right triangle, the cosine of an acute angle is the ratio of the adjacent side/hypotenuse.

Tangent - In a right triangle, the tangent of an acute angle is the ratio of the opposite side/adjacent side.

Complementary angles - two angles whose measures add to 90 degrees

Pythagorean Theorem - states that the sum of the squares of the legs of a right triangle is equal to the square of the length of the hypotenuse. When the legs of the right triangle are labeled "a" and "b" and the hypotenuse is labeled "c", the formula is: LaTeX: a^2+b^2=c^2 .

Similar Triangles - triangles whose corresponding angles are the same measure and whose corresponding sides are proportional

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