Exploring 30-60-90 Triangles

Suppose the measure of angle A is x. What would the measure of angle B be (in terms of x)?

Again, suppose the measure of angle A is x. What would the measure of angle C be (in terms of x)?

Take your responses to the first 2 questions and write an equation, in terms of x, that expresses the relationship among the 3 angle measures of this triangle. What is the value of x? What are the measures of this triangle's 3 angles?

How does the length of the hypotenuse of this triangle compare with the length of this triangle's shorter leg?

Suppose the shorter leg's length (BC) = 4 cm. What would AB be?

Take the information from the previous question. Use this information to write (and solve) an equation in order to find AC. Write this distance in simple radical form.

Suppose BC = 5. What is AB? Use this information to solve for AC in simple radical form.

Suppose BC = 6. What is AB? Use this information to solve for AC in simple radical form.

Suppose BC = 7. What is AB? Use this information to solve for AC in simple radical form.

For any 30-60-90 triangle, what does the ratio equal?

For any 30-60-90 triangle, what does the ratio equal?

For any 30-60-90 triangle, what does the ratio equal?