Question

name: clark
lesson 3.2.3 assignment
date: 16/16/15
period: 3
3 - 93. ben thinks that the slope ratio for this triangle is $\frac{7}{10}$. carlissa thinks the ratio is $\frac{10}{7}$. who is correct? explain your thinking fully.
homework help

Explanation:

Step1: Recall the formula for slope ratio

The slope ratio (also known as the tangent of an angle in a right - triangle) is given by \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Identify the angle for slope ratio

The slope ratio is usually calculated with respect to the angle of inclination. If we consider the non - right angle (let's assume the angle of inclination), and if we take the vertical side as the opposite side and the horizontal side as the adjacent side. Here, if we assume the standard orientation (vertical change over horizontal change), for a right - triangle, the slope \(m = \frac{\text{rise}}{\text{run}}\). The vertical side (rise) is \(7\) and the horizontal side (run) is \(10\). So, using the formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\) (in the context of a right - triangle representing a slope, where the vertical change is \(y\) and horizontal change is \(x\)), we have \(m=\frac{7}{10}\).

Answer:

Ben is correct. The slope ratio (which can be thought of as the ratio of the vertical change to the horizontal change in a right - triangle representing a slope) is \(\frac{7}{10}\) since the formula for slope \(m=\frac{\text{vertical change}}{\text{horizontal change}}\) and here the vertical side length is \(7\) and the horizontal side length is \(10\).