Question

1. a. write a plan of attack. how are you going to find the grade of trail 3 (swift fox)?

the plan of attack must include the following:

• list of information you need to find to solve the problem
• explanation of your plan of attack, which includes
• how to find the unknowns
• why you need each unknown

hint: slope = \\( \frac{rise}{run} \\) and slope = tan (a)

Explanation:

To find the grade (slope) of Trail 3 (Swift Fox), we need to know the angle \(A\) (or be able to calculate it) or the values of \(h_1\) (rise) and the horizontal run (adjacent side to angle \(A\)). If we know angle \(A\), we can directly use the formula \(slope=\tan(A)\). If we don't know angle \(A\) but can find \(h_1\) (using trigonometric relations in the right - triangle formed, for example, if we assume some other known angles or side - length ratios) and the horizontal run (maybe by using Pythagorean theorem if other sides are known or by splitting the base of the large triangle into parts and relating them), we can use \(slope = \frac{rise}{run}=\frac{h_1}{run}\).

Answer:

We need either the angle \(A\) (to use \(slope=\tan(A)\)) or the values of \(h_1\) (rise) and the horizontal run (to use \(slope=\frac{h_1}{run}\)). If angle \(A\) is unknown, we can find \(h_1\) (e.g., using \(\sin(A)=\frac{h_1}{590}\) if we can find \(A\) from other geometric properties of the figure like similar triangles or angle - sum properties of the large triangle) and the run (e.g., using \(\cos(A)=\frac{run}{590}\) or by subtracting known segments of the base from the total base length if the base of the large triangle is composed of multiple parts). Then apply the slope formula.