Question

b. 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?

Explanation:

Step1: Recall the slope ratio formula

The slope ratio \(\frac{\Delta y}{\Delta x}\) for a right - triangle is equivalent to \(\tan\theta\), where \(\theta\) is the non - right angle.

Step2: Calculate \(\tan19^{\circ}\)

We know that \(\tan19^{\circ}\approx0.3443\) (using a calculator: \(\tan x=\frac{\sin x}{\cos x}\), and for \(x = 19^{\circ}\), \(\sin19^{\circ}\approx0.3256\), \(\cos19^{\circ}\approx0.9455\), \(\tan19^{\circ}=\frac{\sin19^{\circ}}{\cos19^{\circ}}\approx\frac{0.3256}{0.9455}\approx0.3443\)).
Since \(0.3443
eq2.675\), Lyra's answer is wrong.

Answer:

Isiah is right. Because the slope ratio \(\frac{\Delta y}{\Delta x}\) for the given triangle (where the non - right angle is \(19^{\circ}\)) is \(\tan19^{\circ}\approx0.3443
eq2.675\).