Right Triangle Trigonometry: Missing Sides and Angles

Right Triangle Trigonometry

Right Triangles are SPECIAL triangles!

Objectives

• SWBAT learn the Pythagorean theorem, its origins, and how to apply it in finding missing side lengths to understand the relationship between the legs and hypotenuse of the right triangle

• SWBAT learn about trigonometric functions and discerning which is which and manipulating the function to solve for missing side lengths and angles

• SWBAT discuss with their peers in their groups about the content using Trigonometric and Pythagorean Theorem Terminology in order to solve for the missing sides/angles and being able to explain to the whole class

Match

Match the following:

leg

leg

hypotenuse

• leg

• leg

• hypotenuse

Multiple Choice

True or False:

The Pythagorean theorem works for ALL types of triangles, not just right angles.

• TRUE

• FALSE

Multiple Choice

What does the 'c' in the Pythagorean formula stand for?

• Leg

• Hypotenuse

• Angle

• None of the Above

Multiple Choice

Which side of the triangle is the longest?

• Hypotenuse

• Leg

• Angle

• None of the Above

Reorder

Reorder the following to Reflect the Pythagorean Theorem:

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Multiple Choice

'a' and 'b' are the ___________ of the triangle?

• hypotenuse

• angles

• legs

• all of the above

If the square of the hypotenuse equals the sum of the squares of the other two legs, then the triangle is a right triangle.

You can also use the Pythagorean Theorem to determine whether a triangle is a right triangle.

Converse of the Pythagorean Theorem

Multiple Choice

This is a right triangle.

• True

• False

• Hypotenuse is the side opposite of the 90-degree angle in a right triangle

• Adjacent side is the leg next to an acute angle in a right triangle that is not the hypotenuse

• Opposite side of the side across from an angle in a triangle

Sin (B)=

Cos (B)=

Tan (B)=

What are the Trigonometric Ratios?

​Sin (A)=

Cos (A)=

Tan (B)=

What are the Trigonometric Ratios?

Match

Match the following:

• cos( $$\alpha$$ )

• sin( $$\alpha$$ )

• tan( $$\alpha$$ )

• $$\frac{\text{15}}{\text{17}}$$

• $$\frac{\text{8}}{\text{17}}$$

• $$\frac{8}{15}$$

​CSC- Cosectant: Reciprocal of Sin

SEC- Sectant: Reciprocal of Cos

COT- Cotangent: Reciprocal of Tan

​Reciprocal Trigonometric Functions

Match

Match the following:

• cot( $$\alpha$$ )

• csc( $$\alpha$$ )

• sec( $$\alpha$$ )

• $$\frac{15}{8}$$

• $$\frac{\text{17}}{\text{8}}$$

• $$\frac{\text{17}}{\text{15}}$$

PRACTICE PROBLEMS