Question

1. (4 - 28) a. thalia did not have a tool to help her find the slope angle in the triangle at right. however, she claims that the slope angle has to be more than 45°. do you agree with thalia?

Explanation:

Step1: Recall tangent - slope relationship

The slope of a line in a right - triangle is given by the tangent of the angle it makes with the horizontal. Let the angle be $\theta$. Then $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Calculate the tangent of the angle

In the given right - triangle, the opposite side to the angle $\theta$ is 6 and the adjacent side is 4. So, $\tan\theta=\frac{6}{4} = 1.5$.

Step3: Compare with $\tan45^{\circ}$

We know that $\tan45^{\circ}=1$. Since the tangent function $y = \tan x$ is an increasing function for $0^{\circ}1$, then $\theta > 45^{\circ}$.

Answer:

Yes, I agree with Thalia.