Pythagoras' Theorem and Trigonometry

Question 1

What shape does Pythagoras’ theorem involve?

Answer 1

Pythagoras’ theorem involves right angle triangles

Question 2

What are the sides labelled in Pythagoras’ theorem?

Answer 2

A, B and C. A and B are inter changeable and are used for the 2 shorter sides. C is used for the longest side (hypotenuse)

Question 3

What is the formula for Pythagoras’ Theorem?

Answer 3

a^2 + b^2 = c^2

Question 4

What are the steps in finding the length of the longer side (labelled C)?

Answer 4

To find the longer side length labelled C, you:
- State the formula
- Substitute the values
- Solve

Question 5

What are the steps in finding the length of the shorter side (labelled A or B)?

Answer 5

To find the shorter side length labelled A or B, you:
- State the formula
- Substitute the values
- Solve by using the inverse

Question 6

What is the side length labelled H and where can you find it?

Answer 6

The side length labelled H is the hypotenuse. The hypotenuse can be found opposite the right angle.

Question 7

What is the side length labelled O and where can you find it?

Answer 7

The side length labelled O is the opposite. The opposite can be found opposite the other angle.

Question 8

What is the side length labelled A and where can you find it?

Answer 8

The side length labelled A is the adjacent. The adjacent is the left over angle that isn’t opposite to the other 2 angles.

Question 9

What is the phrase used to remember trigonometric ratios?

Answer 9

SohCahToa

Question 10

What are the 3 trigonometric ratios?

Answer 10

The 3 trigonometric ratios are:

sin (θ) = o/h
cos (θ) = a/h
tan (θ) = o/a

Question 11

What are the steps to finding an unknown side length?

Answer 11

The steps to finding an unknown side length are:

• Labelling the known sides with H,O,A
• Stating the correct trig ratio
• Substituting the values
• Solve the equation and round the answer if asked

Question 12

What is an example of an equation that you would put into the calculator when finding the unknown side length?

Answer 12

17sin(34) = x

Question 13

What are the steps to finding an unknown angle?

Answer 13

The steps to finding an unknown angle are:

• Labelling the known sides with H,O,A
• Stating the correct trig ratio
• Substituting the values
• Do the inverse (-1)
• Solve in calculator and round if asked

Question 14

What is an example of an equation that you would put into the calculator when finding the unknown angle?

Answer 14

θ = sin ^-1 (1/2)

Question 15

What are the steps to solving for the denominator?

Answer 15

The steps for solving for the denominator are:

• Labelling the known sides with H,O,A
• Stating the correct trig ratio
• Substituting the values
• Swap ‘x’ with the equation on the left hand side
• Solve in calculator and round if asked

Question 16

What is an example of an equation that you would put into the calculator when solving for the denominator?

Answer 16

x = 5 ÷ cos (30)

(Questions are in fraction form so it would be 5 over cos(30) instead to put into the calculator)

Question 17

What does the theta symbol represent (θ)?

Answer 17

The theta symbol represents an angle that is unknown.

Question 18

Angles of elevation must be above the _ line.

Answer 18

Horizontal

Question 19

Angles of depression must be _ the horizontal line.

Answer 19

Below

Question 20

What are the steps in finding the angle of elevation/depression?

Answer 20

The steps to find the angle of elevation/depression are:

• Read the worded problem
• Highlight/underline any important information
• Draw a diagram (with the horizontal line)
• Create the triangle
• Solve for x and round the answer if necessary
• Write the answer in words relating to the problem