Exploring Sine with similar triangles
Tasks
Getting started,
The upper corner contains 3 adjustable sliders
-Slider adjusts the angle for the similar triangles
-Slider Length AC changes the length of the adjacent for the triangle ABC
-Slider Length AE changes the length of the adjacent for the triangle ADE
Task 1.
Adjust your angle slider to 30 , what trigonometric ratio do you see, is this what you expected?
Compare the length of the opposite to the length of the hypotenuse for the ABC triangle?
Compare the length of the opposite to the length of the hypotenuse for the ADE triangle?
How many times smaller is the opposite compared to the hypotenuse?
(What would you need to multiply the hypotenuse by to find the length of the opposite)
Where else have we seen this number?
If you change the LengthAC and LengthAE for each triangles, does this change?
Task 2.
Adjust your angle to another angle between 15 and 40.
What is the new Trigonometric ratio for the Sine of your new angle?
How many times smaller is the opposite compared to the hypotenuse for this angle?
(What would you need to multiply the hypotenuse by to find the length of the opposite)
What do you think this means? (check with the teacher before moving onto the Cosine sheet)