Trigonometry
(Relations between elements of a triangle.)
Have you ever noticed:
All triangles have 3 sides and 3 angles.
If you make any side of your triangle longer, the angle opposite to that side also increases in measure. What else have you noticed about the measures of triangles and how they are related?
Right Triangles – S O H C A H T O A
(sine / cosine / tangent)
Exercise 1:
Find the hypotenuse in the following triangles and label it with an “H”.
(a)/ (b) / (c)
(d) / (e) / (f)
(g) / (h) / (i)
Exercise 2:
θ is the symbol for the eighth letter of the Greek alphabet. It is called, theta. Theta is the symbol that we will use to represent the measure of an angle in a triangle.
A. Which angle are we never using θ to represent in our triangles above? ______
B. Find the side opposite the θ angles in our triangles above and label that side “O”.
C. Find the side adjacent to the θ angles in our triangles above and label that side “A”.
Exercise 3:
A. Figure out how YOUR calculator works. Make sure that you can get the result shown below:
sin 56 = 8290376
B. Calculate the following to 4 decimal places.
(a) sin 45 = ______
(b) cos 45 = ______
(c) tan 45 = ______
Exercise 4:
How does this help us to find measures in triangles?
Find x.
Follow these steps:
1. Label the hypotenuse with “H”.
2. Label the other two sides with “O” & “A” paying attention to the location of θ (the angle with the measure in this case).
3. Eliminate the side without the measure. The sides with the measures are _____ & _____.
4. Circle the acronym below which has the two letters from #3 in it:
S OH C AH T OA
5. Circle the corresponding formula to match the acronym which you found in #4:
6. Calculate the value of x.
Think about how you would solve a ratio problem:
Exercise 5:
Complete the following text book questions:
pages 362-363 #3, 6, 7, 9, 10, 11