Question

3 - 94. use your observations from problem 3 - 92 to answer the following questions: homework help
thalia did not have a tool to help her determine the slope angle θ in the
a. triangle at right. however, she claims that the slope angle has to be more than
45°. do you agree with thalia? why?

Explanation:

Step1: Recall the property of right - angled triangles

In a right - angled triangle, if the two legs are equal (\(a = b\)), then the non - right angles are \(45^{\circ}\) each. The tangent of an angle \(\theta\) in a right - angled triangle is given by \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Analyze the given triangle

Here, the opposite side to the angle \(\theta\) (assuming the side of length \(6\) is opposite) and the adjacent side is \(4\). So, \(\tan\theta=\frac{6}{4} = 1.5\).
We know that \(\tan45^{\circ}=1\). Since the tangent function \(y = \tan x\) is an increasing function for \(0^{\circ}

Answer:

Yes, we agree with Thalia. Because in a right - angled triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), here \(\tan\theta=\frac{6}{4}=1.5\) and \(\tan45^{\circ} = 1\). Since the tangent function is increasing for \(0^{\circ}<\theta<90^{\circ}\), and \(1.5>1\), so \(\theta>45^{\circ}\).