CPM Homework Help : INT2 Problem 3-94

Use your observations from problem 3-92 to answer the following questions:

Thalia did not have a tool to help her determine the slope angle $θ$ in the triangle at right. However, she claims that the slope angle has to be more than $45^\circ$ . Do you agree with Thalia? Why?
Hint (a):
An isosceles right triangle has a slope of $1$ and slope angle of $45^\circ$ . Does this triangle have a larger or smaller ratio? What does this tell us about the slope angle?
Answer (a):
Yes, because the slope ratio is greater than $1$ ,the angle must be greater than $45^\circ$ .

A right triangle with a base of 4 and height of 6.

Lyra was trying to determine the slope ratio for the triangle at right, and she says the answer is $\frac { \Delta y } { \Delta x }= 2.675$ . Isiah claims that cannot be correct. Who is right? How do you know?
Hint (b):
Use the same method as in part (a).

A right triangle with a 19 degree angle.

Without determining the actual value, what information do you know about $x$ in the diagram at right?
Hint (c):
If the slope angle is $76^\circ$ , is the slope ratio more than $1$ or less than $1$ ?
Does this mean that $x$ is greater than $9$ or less than $9$ ?

A right triangle with a base of x and height of 9. 76 degrees angle is in between the hypotenuse and base.