Copy of Trigonometric Ratios in Right Triangles
What do you notice about the two triangles?
If Angle A in Triangle 1 is your reference angle, what is the length of the opposite side?
If Angle B in Triangle 1 is your reference angle, what is the length of the opposite side?
Predict the value of [i]x.[/i]
Discover [color=#0000ff]sine[/color], [color=#ff0000]cosine[/color], and [color=#00ff00]tangent [/color]ratios in right triangles. Observe how these ratios change when modifying the triangle. Make sure to use the drop-down menu to explore all three types of ratios. Also, make sure to click the purple [color=#9900ff]Animate [/color]button.
Putting It All Together
[i]Answer these open ended questions on your own or with others to form deeper math connections.[/i]
In a 3, 4, 5 right triangle, what is the sine ratio when the reference angle is adjacent to the side of length 3?
In a 3, 4, 5 right triangle, what is the sine ratio when the reference angle is adjacent to the side of length 4?
In a 3, 4, 5 right triangle, what is the what is the tangent ratio when the reference angle is adjacent to the side of length 3?
In a 3, 4, 5 right triangle, what is the what is the tangent ratio when the reference angle is adjacent to the side of length 4?
In a 3, 4, 5 right triangle, what is the cosine ratio when the reference angle is adjacent to the side of length 3?
In a 3, 4, 5 right triangle, what is the cosine ratio when the reference angle is adjacent to the side of length 4?
Extension: How can you use the sine function to find the exact value of x? What is the exact value of x?